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  </span><![endif]><![if !mso & !vml]>&nbsp;<![endif]><![if !vml]></td>
 </tr>
</table>

</span></span><![endif]><!--[if gte vml 1]><v:shape id=3D"_x0000_s1107" typ=
e=3D"#_x0000_t202"
 style=3D'position:absolute;margin-left:-18.75pt;margin-top:-57.4pt;width:1=
75.75pt;
 height:85.05pt;z-index:1;mso-wrap-distance-left:2.88pt;
 mso-wrap-distance-top:2.88pt;mso-wrap-distance-right:2.88pt;
 mso-wrap-distance-bottom:2.88pt' filled=3D"f" stroked=3D"f" insetpen=3D"t"
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 <v:shadow color=3D"#ccc"/>
 <v:textbox style=3D'mso-column-margin:2mm' inset=3D"2.88pt,2.88pt,2.88pt,2=
.88pt"/>
</v:shape><![endif]--><![if !vml]><span style=3D'mso-ignore:vglayout;positi=
on:
relative;z-index:1'><span style=3D'position:absolute;left:-25px;top:-77px;
width:238px;height:118px'>

<table cellpadding=3D0 cellspacing=3D0>
 <tr>
  <td width=3D238 height=3D118 style=3D'vertical-align:top'><![endif]><![if=
 !mso]><span
  style=3D'position:absolute;mso-ignore:vglayout;z-index:1'>
  <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
   <tr>
    <td><![endif]>
    <div v:shape=3D"_x0000_s1107" style=3D'padding:2.88pt 2.88pt 2.88pt 2.8=
8pt'
    class=3Dshape>
    <p class=3DMsoNormal style=3D'mso-pagination:none'><span lang=3DEN-US
    style=3D'font-size:72.0pt;mso-ansi-language:EN-US'>IST<o:p></o:p></span=
></p>
    </div>
    <![if !mso]></td>
   </tr>
  </table>
  </span><![endif]><![if !mso & !vml]>&nbsp;<![endif]><![if !vml]></td>
 </tr>
</table>

</span></span><![endif]><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:16.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>tel<o:p>=
</o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:16.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;
</span><o:p></o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:16.0pt'><span style=3D'mso-spacerun:yes'>&nbsp;</span>Ti=
tle: Electromagnetic
Waves and Physical Reality<o:p></o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:16.0pt'><span style=3D'mso-spacerun:yes'>&nbsp;</span>Jo=
urnal: AIP
Mathematical Physics <o:p></o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>By Professor Kwaku Boateng</span></b><span style=3D'font-size:14.0pt=
'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;</span>Tel<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>00233 243 241 943<span
style=3D'mso-spacerun:yes'>&nbsp; </span><o:p></o:p></span></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;
</span></span></b><span style=3D'font-size:14.0pt'>00233 20 274 8355<b
style=3D'mso-bidi-font-weight:normal'><o:p></o:p></b></span></p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Email: <a href=3D"mailto:info@newquantummechanics.com">info@newquant=
ummechanics.com</a></p>

<p class=3DMsoNormal><u><span style=3D'font-size:16.0pt'><o:p><span
 style=3D'text-decoration:none'>&nbsp;</span></o:p></span></u></p>

<p class=3DMsoNormal>The equation given in fig 1.0.1 was derived by Schrodi=
nger.
Neil Bohr, and Max Born gave probability solution backed by <st1:place w:st=
=3D"on"><st1:City
 w:st=3D"on">Copenhagen</st1:City></st1:place> interpretation, which conclu=
ded
that no quantum state would fit a physical realty. This new solution seems =
to cast
new light onto the problem by introducing solution of Schrodinger and
Dirac&#8217;s relativistic equation without probability.</p>

<p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'font-size:16.0pt'>New Solution<o:p></o:p></span></b>=
</p>

<p class=3DMsoNormal style=3D'text-align:justify'>The new solution given by
Professor Kwaku Boateng has many benefits in cosmology, big bang, black hol=
e,
string theory, atom smashing, paranormal studies etc. </p>

<div style=3D'mso-element:para-border-div;border:none;border-bottom:double =
windowtext 2.25pt;
padding:0cm 0cm 1.0pt 0cm'>

<p class=3DMsoNormal style=3D'text-align:justify;border:none;mso-border-bot=
tom-alt:
double windowtext 2.25pt;padding:0cm;mso-padding-alt:0cm 0cm 1.0pt 0cm'>Her=
e we
are will be looking at how his new theory relates to physical reality.</p>

</div>

<p class=3DMsoNormal style=3D'text-align:justify'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal style=3D'text-align:justify'><o:p>&nbsp;</o:p></p>

<table class=3DMsoNormalTable border=3D1 cellspacing=3D0 cellpadding=3D0 wi=
dth=3D461
 style=3D'width:345.6pt;border-collapse:collapse;border:none;mso-border-alt=
:solid windowtext .5pt;
 mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-border-insid=
eh:
 .5pt solid windowtext;mso-border-insidev:.5pt solid windowtext'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'>
  <td width=3D461 valign=3Dtop style=3D'width:345.6pt;border:solid windowte=
xt 1.0pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
  style=3D'font-size:16.0pt;mso-no-proof:yes'><!--[if gte vml 1]><v:shapety=
pe
   id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelativ=
e=3D"t"
   path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" stroked=3D"f">
   <v:stroke joinstyle=3D"miter"/>
   <v:formulas>
    <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/>
    <v:f eqn=3D"sum @0 1 0"/>
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    <v:f eqn=3D"prod @3 21600 pixelWidth"/>
    <v:f eqn=3D"prod @3 21600 pixelHeight"/>
    <v:f eqn=3D"sum @0 0 1"/>
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    <v:f eqn=3D"prod @7 21600 pixelWidth"/>
    <v:f eqn=3D"sum @8 21600 0"/>
    <v:f eqn=3D"prod @7 21600 pixelHeight"/>
    <v:f eqn=3D"sum @10 21600 0"/>
   </v:formulas>
   <v:path o:extrusionok=3D"f" gradientshapeok=3D"t" o:connecttype=3D"rect"=
/>
   <o:lock v:ext=3D"edit" aspectratio=3D"t"/>
  </v:shapetype><v:shape id=3D"_x0000_i1025" type=3D"#_x0000_t75" style=3D'=
width:370.5pt;
   height:119.25pt;visibility:visible'>
   <v:imagedata src=3D"reality_files/image001.jpg" o:href=3D"mhtml:file://F=
:\universal_websites\word_pages_=3D20062008\wordintroductiontoquantummechan=
ics.mht!http://www.physlink.com/Education/AskExperts/Images/ae329a.jpg"/>
  </v:shape><![endif]--><![if !vml]><img border=3D0 width=3D494 height=3D159
  src=3D"reality_files/image002.jpg" v:shapes=3D"_x0000_i1025"><![endif]></=
span></b><b
  style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:20.0pt'><o=
:p></o:p></span></b></p>
  </td>
 </tr>
</table>

<p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'font-size:20.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span></span></b></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Fig 1.0.1</p>

<p><span class=3Dgoogqs-tidbit1><span lang=3DEN-US>In order to extend
Schr&ouml;dinger's formalism to include relativity, the physical picture mu=
st
be altered. The Klein-Gorden equation </span></span><span lang=3DEN-US>uses=
 the relativistic
mass-energy relation:</span></p>

<p class=3DMsoNormal style=3D'margin-left:36.0pt'><span style=3D'mso-no-pro=
of:yes'><!--[if gte vml 1]><v:shape
 id=3D"Picture_x0020_1" o:spid=3D"_x0000_i1026" type=3D"#_x0000_t75" alt=3D=
"E^2 =3D p^2c^2 + m^2c^4\,"
 style=3D'width:111pt;height:16.5pt;visibility:visible'>
 <v:imagedata src=3D"reality_files/image003.gif" o:title=3D","/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D148 height=3D22
src=3D"reality_files/image003.gif" alt=3D"E^2 =3D p^2c^2 + m^2c^4\," v:shap=
es=3D"Picture_x0020_1"><![endif]></span></p>

<p><span lang=3DEN-US>to produce the differential equation</span></p>

<table class=3DMsoNormalTable border=3D1 cellspacing=3D0 cellpadding=3D0 wi=
dth=3D319
 style=3D'width:239.3pt;border-collapse:collapse;border:none;mso-border-alt=
:solid windowtext .5pt;
 mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-border-insid=
eh:
 .5pt solid windowtext;mso-border-insidev:.5pt solid windowtext'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'>
  <td width=3D319 valign=3Dtop style=3D'width:239.3pt;border:solid windowte=
xt 1.0pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal><span style=3D'mso-no-proof:yes'><!--[if gte vml 1]>=
<v:shape
   id=3D"Picture_x0020_2" o:spid=3D"_x0000_i1027" type=3D"#_x0000_t75" alt=
=3D"- \frac{1}{c^2}{\partial^2 \over \partial t^2}\psi =3D  - \nabla^2 \psi=
 + \frac{m^2c^2}{\hbar^2} \psi\,"
   style=3D'width:180pt;height:33pt;visibility:visible'>
   <v:imagedata src=3D"reality_files/image004.gif" o:title=3D","/>
  </v:shape><![endif]--><![if !vml]><img border=3D0 width=3D240 height=3D44
  src=3D"reality_files/image004.gif"
  alt=3D"- \frac{1}{c^2}{\partial^2 \over \partial t^2}\psi =3D  - \nabla^2=
 \psi + \frac{m^2c^2}{\hbar^2} \psi\,"
  v:shapes=3D"Picture_x0020_2"><![endif]></span><b style=3D'mso-bidi-font-w=
eight:
  normal'><span style=3D'font-size:20.0pt'><o:p></o:p></span></b></p>
  </td>
 </tr>
</table>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>FIG 1.0 .2=
</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>which is relativistically invariant.</p>

<p><span lang=3DEN-US>This equation has been solved at length in other arti=
cle so
only the results will be quoted here see the table below..</span></p>

<p><span lang=3DEN-US><span style=3D'mso-spacerun:yes'>&nbsp;</span>(1) For=
 a=3DL the
energy is given as &nbsp;</span></p>

<p class=3Dparagraph><sub><span lang=3DEN-US style=3D'mso-ansi-language:EN-=
US;
mso-fareast-language:EN-US;mso-no-proof:yes'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;
</span><!--[if gte vml 1]><v:shape id=3D"Picture_x0020_5" o:spid=3D"_x0000_=
i1028"
 type=3D"#_x0000_t75" style=3D'width:141pt;height:33pt;visibility:visible'>
 <v:imagedata src=3D"reality_files/image005.gif" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D188 height=3D44
src=3D"reality_files/image005.gif" v:shapes=3D"Picture_x0020_5"><![endif]><=
/span></sub><span
lang=3DEN-US style=3D'mso-ansi-language:EN-US'><o:p></o:p></span></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center;tab-stops:10=
2.0pt'><i
style=3D'mso-bidi-font-style:normal'><span style=3D'font-family:Tahoma'>TAB=
LE OF
SOLUTIONS<o:p></o:p></span></i></p>

<table class=3DMsoNormalTable border=3D1 cellspacing=3D0 cellpadding=3D0
 style=3D'border-collapse:collapse;border:none;mso-border-alt:solid windowt=
ext .5pt;
 mso-yfti-tbllook:480;mso-padding-alt:0cm 5.4pt 0cm 5.4pt;mso-border-inside=
h:
 .5pt solid windowtext;mso-border-insidev:.5pt solid windowtext'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td valign=3Dtop style=3D'border:solid windowtext 1.0pt;mso-border-alt:so=
lid windowtext .5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>CASE<o:p></o:p></span></p>
  </td>
  <td valign=3Dtop style=3D'border:solid windowtext 1.0pt;border-left:none;
  mso-border-left-alt:solid windowtext .5pt;mso-border-alt:solid windowtext=
 .5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>HERMITIAN
  CONDITIONS<o:p></o:p></span></p>
  </td>
  <td width=3D124 valign=3Dtop style=3D'width:93.2pt;border:solid windowtex=
t 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>NEW
  SOLUTION<o:p></o:p></span></p>
  </td>
  <td width=3D236 valign=3Dtop style=3D'width:176.9pt;border:solid windowte=
xt 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>ENERGY=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<span
  style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
  </span><o:p></o:p></span></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:1'>
  <td valign=3Dtop style=3D'border:solid windowtext 1.0pt;border-top:none;
  mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext =
.5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>1<o:p></o:p></span></p>
  </td>
  <td valign=3Dtop style=3D'border-top:none;border-left:none;border-bottom:=
solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;mso-border-top-alt:solid windowtext .=
5pt;
  mso-border-left-alt:solid windowtext .5pt;mso-border-alt:solid windowtext=
 .5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal>Y(0)=3DY(1)=3D0<span lang=3DEN-US style=3D'mso-ansi-=
language:EN-US;
  mso-fareast-language:EN-US'><o:p></o:p></span></p>
  <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'>Y&#8217;(0)=3Dconstant<s=
pan
  style=3D'font-family:Tahoma'><o:p></o:p></span></p>
  </td>
  <td width=3D124 valign=3Dtop style=3D'width:93.2pt;border-top:none;border=
-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p><span lang=3DEN-US>(d/n&#960;)*sin((n&#960;x)</span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'><o:p>&nbsp;</o:p></span></p>
  </td>
  <td width=3D236 valign=3Dtop style=3D'width:176.9pt;border-top:none;borde=
r-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><b style=3D'mso-bidi-fon=
t-weight:
  normal'>En=3D</b><span style=3D'font-size:22.0pt'> (n<sup>2</sup>&#960;<s=
up>2</sup>
  h<sup>2</sup> )/(2m)</span><span style=3D'font-family:Tahoma'><o:p></o:p>=
</span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'><o:p>&nbsp;</o:p></span></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:2'>
  <td valign=3Dtop style=3D'border:solid windowtext 1.0pt;border-top:none;
  mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext =
.5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>2<o:p></o:p></span></p>
  </td>
  <td valign=3Dtop style=3D'border-top:none;border-left:none;border-bottom:=
solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;mso-border-top-alt:solid windowtext .=
5pt;
  mso-border-left-alt:solid windowtext .5pt;mso-border-alt:solid windowtext=
 .5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal>Y&#8217;(0)=3DY(1)=3D0<span lang=3DEN-US style=3D'ms=
o-ansi-language:
  EN-US;mso-fareast-language:EN-US'><o:p></o:p></span></p>
  <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
  <p class=3DMsoNormal>Y&#8217;(1)=3Dcons<span style=3D'font-size:18.0pt'><=
o:p></o:p></span></p>
  </td>
  <td width=3D124 valign=3Dtop style=3D'width:93.2pt;border-top:none;border=
-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p><span lang=3DEN-US>(d/n&#960;)*sin((n&#960;x)</span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'><o:p>&nbsp;</o:p></span></p>
  </td>
  <td width=3D236 valign=3Dtop style=3D'width:176.9pt;border-top:none;borde=
r-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><b style=3D'mso-bidi-fon=
t-weight:
  normal'>En=3D</b><span style=3D'font-size:22.0pt'> (k<sup>2</sup>&#960;<s=
up>2</sup>
  h<sup>2</sup> )/(2m)</span><span style=3D'font-family:Tahoma'><o:p></o:p>=
</span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'><o:p>&nbsp;</o:p></span></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:3'>
  <td valign=3Dtop style=3D'border:solid windowtext 1.0pt;border-top:none;
  mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext =
.5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>3<o:p></o:p></span></p>
  </td>
  <td valign=3Dtop style=3D'border-top:none;border-left:none;border-bottom:=
solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;mso-border-top-alt:solid windowtext .=
5pt;
  mso-border-left-alt:solid windowtext .5pt;mso-border-alt:solid windowtext=
 .5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal>Y(0)=3DY&#8217;(1)=3D0<span lang=3DEN-US style=3D'ms=
o-ansi-language:
  EN-US;mso-fareast-language:EN-US'><o:p></o:p></span></p>
  <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'>Y&#8217;(0)=3Dconstant<s=
pan
  style=3D'font-family:Tahoma'><o:p></o:p></span></p>
  </td>
  <td width=3D124 valign=3Dtop style=3D'width:93.2pt;border-top:none;border=
-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p><span lang=3DEN-US>(d/k&#960;)*sin((k&#960;x)</span></p>
  <p><span lang=3DEN-US style=3D'font-family:Tahoma'>k=3D(2n+1)/2<o:p></o:p=
></span></p>
  </td>
  <td width=3D236 valign=3Dtop style=3D'width:176.9pt;border-top:none;borde=
r-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><b style=3D'mso-bidi-fon=
t-weight:
  normal'>En=3D</b><span style=3D'font-size:22.0pt'> (n<sup>2</sup>&#960;<s=
up>2</sup>
  h<sup>2</sup> )/(2m)</span><span style=3D'font-family:Tahoma'><o:p></o:p>=
</span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'>k=3D(2n+1)/2<o:p></o:p></span></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:4;mso-yfti-lastrow:yes'>
  <td valign=3Dtop style=3D'border:solid windowtext 1.0pt;border-top:none;
  mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext =
.5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'>F<span style=3D'font-fam=
ily:Tahoma'>4<o:p></o:p></span></p>
  </td>
  <td valign=3Dtop style=3D'border-top:none;border-left:none;border-bottom:=
solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;mso-border-top-alt:solid windowtext .=
5pt;
  mso-border-left-alt:solid windowtext .5pt;mso-border-alt:solid windowtext=
 .5pt;
  padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal>Y&#8217;(0)=3DY(1)=3D0<span lang=3DEN-US style=3D'ms=
o-ansi-language:
  EN-US;mso-fareast-language:EN-US'><o:p></o:p></span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><o:p>&nbsp;</o:p></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'>Y&#8217;(1)=3Dconstant<s=
pan
  style=3D'font-family:Tahoma'><o:p></o:p></span></p>
  </td>
  <td width=3D124 valign=3Dtop style=3D'width:93.2pt;border-top:none;border=
-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p><span lang=3DEN-US>(d/n&#960;)*sin((n&#960;x)</span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'><o:p>&nbsp;</o:p></span></p>
  </td>
  <td width=3D236 valign=3Dtop style=3D'width:176.9pt;border-top:none;borde=
r-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1=
.0pt;
  mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid window=
text .5pt;
  mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 0cm 5.4pt'>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><b style=3D'mso-bidi-fon=
t-weight:
  normal'>En=3D</b><span style=3D'font-size:22.0pt'>((k<sup>2</sup>&#960;<s=
up>2</sup>
  h<sup>2</sup>)/(2m)<o:p></o:p></span></p>
  <p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-fami=
ly:Tahoma'><o:p>&nbsp;</o:p></span></p>
  </td>
 </tr>
</table>

<p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-family=
:Tahoma'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;
</span>Table 5<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-family=
:Tahoma'>of
Schrodinger&#8217;s equation gives one wave function the new one gives two
distinct solutions.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Cases 1, =
2, and
4 give the same eigenfuncion <o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-family=
:Tahoma'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;
</span>Y =3D (d/n</span><span style=3D'font-size:14.0pt'>&#960;)</span><span
style=3D'font-family:Tahoma'> sin(<u>n</u></span><span style=3D'font-size:1=
4.0pt'>&#960;</span><span
style=3D'font-size:16.0pt'>x</span><span style=3D'font-family:Tahoma'>)<o:p=
></o:p></span></p>

<p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-family=
:Tahoma'>while
case 3 gives different eigenfunction<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-family=
:Tahoma'>.
Y<sub>n</sub> =3D 2d/(2n+1)</span><span style=3D'font-size:16.0pt'>&#960;</=
span><span
style=3D'font-size:22.0pt'>)</span><u><span style=3D'font-family:Tahoma'> <=
/span></u><span
style=3D'font-family:Tahoma'>sin (2n+1)</span><span style=3D'font-size:22.0=
pt'> </span><span
style=3D'font-size:16.0pt'>&#960;</span><span style=3D'font-family:Tahoma'>x
/2<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>n =
=3D
0,1,2 -----<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'tab-stops:102.0pt'><span style=3D'font-family=
:Tahoma'>See
example graphs fig 1.4.4 and fig 1.4.5 below which show two waves which are
ninty degrees out of phase.</span><span style=3D'font-size:18.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span></span><span
style=3D'font-family:Tahoma'><o:p></o:p></span></p>

<p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_s1135" type=
=3D"#_x0000_t202"
 style=3D'position:absolute;margin-left:-36pt;margin-top:13.05pt;width:242.=
4pt;
 height:235.2pt;z-index:7;mso-wrap-style:none'>
 <v:textbox style=3D'mso-fit-shape-to-text:t'/>
</v:shape><![endif]--><![if !vml]><span style=3D'mso-ignore:vglayout;positi=
on:
absolute;z-index:7;margin-left:-49px;margin-top:16px;width:329px;height:320=
px'>

<table cellpadding=3D0 cellspacing=3D0>
 <tr>
  <td width=3D329 height=3D320 bgcolor=3Dwhite style=3D'border:.75pt solid =
black;
  vertical-align:top;background:white'><![endif]><![if !mso]><span
  style=3D'position:absolute;mso-ignore:vglayout;z-index:7'>
  <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
   <tr>
    <td><![endif]>
    <div v:shape=3D"_x0000_s1135" style=3D'padding:4.35pt 7.95pt 4.35pt 7.9=
5pt'
    class=3Dshape>
    <p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_i1029" ty=
pe=3D"#_x0000_t75"
     style=3D'width:227.25pt;height:227.25pt'>
     <v:imagedata src=3D"reality_files/image006.png" o:title=3D"graph n equ=
als 1"/>
    </v:shape><![endif]--><![if !vml]><img width=3D303 height=3D303
    src=3D"reality_files/image007.gif" v:shapes=3D"_x0000_i1029"><![endif]>=
</p>
    </div>
    <![if !mso]></td>
   </tr>
  </table>
  </span><![endif]><![if !mso & !vml]>&nbsp;<![endif]><![if !vml]></td>
 </tr>
</table>

</span><![endif]><!--[if gte vml 1]><v:shape id=3D"_x0000_s1134" type=3D"#_=
x0000_t202"
 style=3D'position:absolute;margin-left:225pt;margin-top:8.35pt;width:233.4=
pt;
 height:226.2pt;z-index:6;mso-wrap-style:none'>
 <v:textbox style=3D'mso-fit-shape-to-text:t'/>
</v:shape><![endif]--><![if !vml]><span style=3D'mso-ignore:vglayout;positi=
on:
absolute;z-index:6;margin-left:299px;margin-top:10px;width:317px;height:308=
px'>

<table cellpadding=3D0 cellspacing=3D0>
 <tr>
  <td width=3D317 height=3D308 bgcolor=3Dwhite style=3D'border:.75pt solid =
black;
  vertical-align:top;background:white'><![endif]><![if !mso]><span
  style=3D'position:absolute;mso-ignore:vglayout;z-index:6'>
  <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
   <tr>
    <td><![endif]>
    <div v:shape=3D"_x0000_s1134" style=3D'padding:4.35pt 7.95pt 4.35pt 7.9=
5pt'
    class=3Dshape>
    <p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_i1030" ty=
pe=3D"#_x0000_t75"
     style=3D'width:218.25pt;height:218.25pt'>
     <v:imagedata src=3D"reality_files/image008.png" o:title=3D"graph n equ=
als 2"/>
    </v:shape><![endif]--><![if !vml]><img width=3D291 height=3D291
    src=3D"reality_files/image009.gif" v:shapes=3D"_x0000_i1030"><![endif]>=
</p>
    </div>
    <![if !mso]></td>
   </tr>
  </table>
  </span><![endif]><![if !mso & !vml]>&nbsp;<![endif]><![if !vml]></td>
 </tr>
</table>

</span><![endif]><span style=3D'font-size:18.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
</span><o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><o:p>&nbsp;</o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><o:p>&nbsp;</o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><o:p>&nbsp;</o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'>Fig 1.1.1<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Fig 1.1.2<o:p></o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D<o:p></o:p></span></p>

<p><b style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;
mso-ansi-language:EN-GB;mso-fareast-language:EN-GB'>Electron or Particle Sp=
reads
Through Space</span></b><span style=3D'font-size:18.0pt;mso-ansi-language:E=
N-GB;
mso-fareast-language:EN-GB'>.<o:p></o:p></span></p>

<p><span style=3D'font-size:14.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'>Fig 1.2.1 shows that the Eigen function<o:p></o:p></span></p>

<p><span lang=3DEN-US style=3D'font-size:14.0pt;font-family:Tahoma'>Y =3D (=
d/n</span><span
lang=3DEN-US style=3D'font-size:14.0pt'>&#960;)</span><span lang=3DEN-US
style=3D'font-size:14.0pt;font-family:Tahoma'> sin(<u>n</u></span><span
lang=3DEN-US style=3D'font-size:14.0pt'>&#960;x</span><span lang=3DEN-US
style=3D'font-size:14.0pt;font-family:Tahoma'>)</span><span style=3D'font-s=
ize:
14.0pt;mso-ansi-language:EN-GB;mso-fareast-language:EN-GB'><o:p></o:p></spa=
n></p>

<p><span style=3D'font-size:14.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'>gives two different waves when </span><span lang=3DEN-US style=3D'fo=
nt-size:
14.0pt;font-family:Tahoma'>d/n</span><span lang=3DEN-US style=3D'font-size:=
14.0pt'>&#960;</span><span
lang=3DEN-US style=3D'font-size:14.0pt;mso-ansi-language:EN-GB;mso-fareast-=
language:
EN-GB'> </span><span style=3D'font-size:14.0pt;mso-ansi-language:EN-GB;
mso-fareast-language:EN-GB'>=3D2 and </span><span lang=3DEN-US style=3D'fon=
t-size:
14.0pt;font-family:Tahoma'>d/n</span><span lang=3DEN-US style=3D'font-size:=
14.0pt'>&#960;</span><span
style=3D'font-size:14.0pt;mso-ansi-language:EN-GB;mso-fareast-language:EN-G=
B'> =3D4<o:p></o:p></span></p>

<p><span style=3D'font-size:14.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'>This is saying that relativistically speaking electrons or particles=
 do
spread through space. There is no known limit point set on the value of d. =
This
may require empirical considerations. <o:p></o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><!--[if gte vml 1]><v:shape id=3D"_x0000_i1031" type=3D"#_x0000_t75"
 style=3D'width:375pt;height:375pt'>
 <v:imagedata src=3D"reality_files/image010.gif" o:title=3D"graph spread ex=
ample"/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D500 height=3D500
src=3D"reality_files/image010.gif" v:shapes=3D"_x0000_i1031"><![endif]><o:p=
></o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><span style=3D'mso-spacerun:yes'>&nbsp; </span>Fig 1.2.1<o:p></o:p><=
/span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D<o:p></o:p></span></p>

<p><b style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;
mso-ansi-language:EN-GB;mso-fareast-language:EN-GB'>Physical Reality<o:p></=
o:p></span></b></p>

<p><span style=3D'font-size:14.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'>Fig 1.3.1 is a sketch of the electron or positron as revealed by
relativistic equation of Dirac and Schrodinger. The electron consists of two
waves each diverging and converging at their centre. Perhaps they even form=
 a dipole.
This is under research.<o:p></o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><o:p>&nbsp;</o:p></span></p>

<p><span lang=3DEN-US><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; <=
/span></span></p>

<p><!--[if gte vml 1]><v:shape id=3D"_x0000_s1133" type=3D"#_x0000_t202" st=
yle=3D'position:absolute;
 margin-left:90pt;margin-top:-54pt;width:260.4pt;height:422.7pt;z-index:5;
 mso-wrap-style:none'>
 <v:textbox style=3D'mso-fit-shape-to-text:t'/>
</v:shape><![endif]--><![if !vml]><span style=3D'mso-ignore:vglayout;positi=
on:
relative;z-index:5'><span style=3D'position:absolute;left:119px;top:-73px;
width:353px;height:570px'>

<table cellpadding=3D0 cellspacing=3D0>
 <tr>
  <td width=3D353 height=3D570 bgcolor=3Dwhite style=3D'border:.75pt solid =
black;
  vertical-align:top;background:white'><![endif]><![if !mso]><span
  style=3D'position:absolute;mso-ignore:vglayout;z-index:5'>
  <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
   <tr>
    <td><![endif]>
    <div v:shape=3D"_x0000_s1133" style=3D'padding:4.35pt 7.95pt 4.35pt 7.9=
5pt'
    class=3Dshape>
    <p class=3DMsoNormal><!--[if gte vml 1]><v:shape id=3D"_x0000_i1032" ty=
pe=3D"#_x0000_t75"
     style=3D'width:245.25pt;height:414.75pt'>
     <v:imagedata src=3D"reality_files/image011.jpg" o:title=3D"scan0003"/>
    </v:shape><![endif]--><![if !vml]><img width=3D327 height=3D553
    src=3D"reality_files/image012.jpg" v:shapes=3D"_x0000_i1032"><![endif]>=
</p>
    </div>
    <![if !mso]></td>
   </tr>
  </table>
  </span><![endif]><![if !mso & !vml]>&nbsp;<![endif]><![if !vml]></td>
 </tr>
</table>

</span></span><![endif]><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<br style=3D'mso-ignore:vglayout' clear=3DALL>

<p><b style=3D'mso-bidi-font-weight:normal'><span lang=3DEN-US>K Wave<o:p><=
/o:p></span></b></p>

<p><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p><span lang=3DEN-US><o:p>&nbsp;</o:p></span></p>

<p><b style=3D'mso-bidi-font-weight:normal'><span lang=3DEN-US>B Wave<o:p><=
/o:p></span></b></p>

<p><span lang=3DEN-US><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;
</span></span></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Fig 1,3 .1</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D</p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><o:p>&nbsp;</o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><o:p>&nbsp;</o:p></span></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><o:p>&nbsp;</o:p></span></p>

<p><b style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:18.0pt;
mso-ansi-language:EN-GB;mso-fareast-language:EN-GB'>Axioms<o:p></o:p></span=
></b></p>

<p><span style=3D'font-size:18.0pt;mso-ansi-language:EN-GB;mso-fareast-lang=
uage:
EN-GB'><!--[if gte vml 1]><v:shape id=3D"_x0000_i1033" type=3D"#_x0000_t75"
 style=3D'width:375pt;height:375pt'>
 <v:imagedata src=3D"reality_files/image013.gif" o:title=3D"non probabilist=
ic waves"/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D500 height=3D500
src=3D"reality_files/image013.gif" v:shapes=3D"_x0000_i1033"><![endif]><o:p=
></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;
</span>Fig 1.4.1<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'font-famil=
y:Tahoma'>Let
Y<sub>n</sub> be a set of eigenvectors corresponding to Eigen values </span=
><b
style=3D'mso-bidi-font-weight:normal'>En</b><span style=3D'font-family:Taho=
ma'> of
Schrodinger&#8217;s equation.<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'>Pn(x)=3D<span style=3D'fo=
nt-size:
18.0pt;font-family:Tahoma'>&#8747;</span><span style=3D'font-family:Tahoma'=
>|Y<sub>n</sub>|<sup>2</sup>dx<o:p></o:p></span></p>

<p class=3DMsoNormal style=3D'text-align:justify'><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The term was interpreted as probability function<b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:20.0pt'> </s=
pan></b>This
term was originally interpreted as probability.</p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><u><span style=3D'font-size:20.0pt'><o:p><span style=3D'text-decora=
tion:
 none'>&nbsp;</span></o:p></span></u></b></p>

<p class=3DMsoNormal style=3D'text-align:justify'>In this new approach to q=
uantum
theory, Pn(x) represents a measure of spatial density of the particle(s) and
therefore of matter: that is Pn(x) is the space occupied by the particle and
not probability. </p>

<p class=3DMsoNormal style=3D'text-align:justify'>The following laws of con=
traction
and expansion follow from the definition of Pn(x):<b style=3D'mso-bidi-font=
-weight:
normal'> <o:p></o:p></b></p>

<p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font=
-weight:
normal'>See the graph fig 1.5.1 below.<o:p></o:p></b></p>

<p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font=
-weight:
normal'><o:p>&nbsp;</o:p></b></p>

<p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'mso-spacerun:yes'>&nbsp;</span></b></p>

<h1><span lang=3DEN-US>Contraction of Particle</span><span lang=3DEN-US
style=3D'font-size:14.0pt'><o:p></o:p></span></h1>

<h4><span lang=3DEN-US style=3D'mso-no-proof:yes'><!--[if gte vml 1]><v:sha=
pe id=3D"Picture_x0020_44"
 o:spid=3D"_x0000_i1034" type=3D"#_x0000_t75" style=3D'width:162pt;height:1=
43.25pt;
 visibility:visible'>
 <v:imagedata src=3D"reality_files/image014.emz" o:title=3D"" cropright=3D"=
36167f"/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D216 height=3D191
src=3D"reality_files/image015.gif" v:shapes=3D"Picture_x0020_44"><![endif]>=
</span><span
lang=3DEN-US style=3D'font-size:36.0pt;font-family:Wingdings;mso-ascii-font=
-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:sym=
bol;
mso-symbol-font-family:Wingdings'><span style=3D'mso-char-type:symbol;mso-s=
ymbol-font-family:
Wingdings'>&agrave;</span></span><span lang=3DEN-US><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;
</span><span style=3D'mso-no-proof:yes'><!--[if gte vml 1]><v:shape id=3D"P=
icture_x0020_45"
 o:spid=3D"_x0000_i1035" type=3D"#_x0000_t75" style=3D'width:1in;height:58.=
5pt;
 visibility:visible'>
 <v:imagedata src=3D"reality_files/image016.emz" o:title=3D"" cropright=3D"=
35462f"/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D96 height=3D78
src=3D"reality_files/image017.gif" v:shapes=3D"Picture_x0020_45"><![endif]>=
</span></span></h4>

<h4 style=3D'text-indent:252.0pt'><!--[if gte vml 1]><v:shape id=3D"_x0000_=
s1113"
 type=3D"#_x0000_t202" style=3D'position:absolute;left:0;text-align:left;
 margin-left:45pt;margin-top:4.7pt;width:1in;height:179.9pt;text-indent:0;
 z-index:-4' filled=3D"f" stroked=3D"f"/><![endif]--><![if !vml]><span
style=3D'mso-ignore:vglayout;position:absolute;z-index:-4;left:0px;margin-l=
eft:
60px;margin-top:6px;width:100px;height:244px'>

<table cellpadding=3D0 cellspacing=3D0>
 <tr>
  <td width=3D100 height=3D244 style=3D'vertical-align:top'><![endif]><![if=
 !mso]><span
  style=3D'position:absolute;mso-ignore:vglayout;left:0pt;z-index:-4'>
  <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
   <tr>
    <td><![endif]>
    <div v:shape=3D"_x0000_s1113" style=3D'padding:3.6pt 7.2pt 3.6pt 7.2pt'
    class=3Dshape>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt'>f</span><span lang=3D=
EN-US>
    &lt; </span><span lang=3DEN-US style=3D'font-size:22.0pt'>&#8734;<o:p><=
/o:p></span></h4>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso=
-bidi-font-weight:
    bold'>g</span><span lang=3DEN-US> &lt; </span><span lang=3DEN-US
    style=3D'font-size:22.0pt'>&#8734;<o:p></o:p></span></h4>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso=
-bidi-font-weight:
    bold'>e</span><span lang=3DEN-US> &lt; </span><span lang=3DEN-US
    style=3D'font-size:22.0pt'>&#8734;<o:p></o:p></span></h4>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso=
-bidi-font-weight:
    bold'>t</span><span lang=3DEN-US> &gt; </span><span lang=3DEN-US
    style=3D'font-size:16.0pt;font-weight:normal;mso-bidi-font-weight:bold'=
>0</span><span
    lang=3DEN-US style=3D'font-size:22.0pt'><o:p></o:p></span></h4>
    <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
    </div>
    <![if !mso]></td>
   </tr>
  </table>
  </span><![endif]><![if !mso & !vml]>&nbsp;<![endif]><![if !vml]></td>
 </tr>
</table>

</span><![endif]><span lang=3DEN-US style=3D'font-size:18.0pt'>f</span><span
lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-family:Wingdings;mso-=
ascii-font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:sym=
bol;
mso-symbol-font-family:Wingdings'><span style=3D'mso-char-type:symbol;mso-s=
ymbol-font-family:
Wingdings'>&agrave;</span></span><span lang=3DEN-US> </span><span lang=3DEN=
-US
style=3D'font-size:22.0pt'>&#8734;<o:p></o:p></span></h4>

<h4 style=3D'text-indent:252.0pt'><span lang=3DEN-US style=3D'font-size:18.=
0pt;
font-weight:normal;mso-bidi-font-weight:bold'>g</span><span lang=3DEN-US> <=
/span><span
lang=3DEN-US style=3D'font-family:Wingdings;mso-ascii-font-family:"Times Ne=
w Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span><span
lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-size:22.0pt'>&#8734;<=
o:p></o:p></span></h4>

<h4 style=3D'text-indent:252.0pt'><span lang=3DEN-US style=3D'font-size:18.=
0pt;
font-weight:normal;mso-bidi-font-weight:bold'>e</span><span lang=3DEN-US> <=
/span><span
lang=3DEN-US style=3D'font-family:Wingdings;mso-ascii-font-family:"Times Ne=
w Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span><span
lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-size:22.0pt'>&#8734; =
<o:p></o:p></span></h4>

<h4><span lang=3DEN-US style=3D'font-size:20.0pt'><o:p>&nbsp;</o:p></span><=
/h4>

<h4><span lang=3DEN-US style=3D'font-size:14.0pt'>Fig 1.5.1 f is frequency,=
 g is mass,
e is energy<o:p></o:p></span></h4>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><span
style=3D'font-size:14.0pt'><o:p>&nbsp;</o:p></span></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'>The following=
 laws
govern quantum contraction.<o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><span style=3D'mso-spacerun:yes'>&nbsp;</span>(1) <b
style=3D'mso-bidi-font-weight:normal'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;</span>Energy density En</b>, varies
inversely as Pn(x). <span style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an>(2C)</p>

<p class=3DMsoNormal><span style=3D'mso-spacerun:yes'>&nbsp;</span>(2)<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span><b style=3D'mso-bidi-font-we=
ight:
normal'>Pn(x)</b> is uniform and convergent with respect to n.<span
style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp; </span>(4C)</p>

<p class=3DMsoNormal>(3)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </spa=
n>Yn(x)
is uniform and convergent with respect to n.<span style=3D'mso-tab-count:3'=
>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an>(4CY)</p>

<p class=3DMsoNormal>(4)<span style=3D'mso-spacerun:yes'>&nbsp; </span>For =
any two
given integers k, j where k&lt;j the Schrodinger </p>

<h1><span lang=3DEN-US style=3D'font-size:12.0pt;font-weight:normal;mso-bid=
i-font-weight:
bold'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n>wave
function gives </span><span lang=3DEN-US style=3D'font-size:12.0pt'>Pk(x)&g=
t;Pj(x),
and Ek&lt;Ej</span><span lang=3DEN-US style=3D'font-size:12.0pt;font-weight=
:normal;
mso-bidi-font-weight:bold'><span style=3D'mso-spacerun:yes'>&nbsp; </span>t=
hat is
Ek is <o:p></o:p></span></h1>

<h1><span lang=3DEN-US style=3D'font-size:12.0pt;font-weight:normal;mso-bid=
i-font-weight:
bold'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>divergent<span style=3D'mso-spacerun:yes'>&nbsp; </span>whiles Pk(x)=
 is
convergent.<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span=
><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;</span><span style=3D'mso-tab-count:=
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>(5C)<o:p></o:p></span></h1>

<h1><span lang=3DEN-US style=3D'font-size:12.0pt;font-weight:normal;mso-bid=
i-font-weight:
bold'>(5)<span style=3D'mso-spacerun:yes'>&nbsp; </span>For any two given
integers k, j where k&lt;j the Schrodinger <o:p></o:p></span></h1>

<h1><span lang=3DEN-US style=3D'font-size:12.0pt;font-weight:normal;mso-bid=
i-font-weight:
bold'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp; </span>wave
function gives </span><span lang=3DEN-US style=3D'font-size:12.0pt'>Yk(x)&g=
t;Yj(x),
and Ek&lt;Ej</span><span lang=3DEN-US style=3D'font-size:12.0pt;font-weight=
:normal;
mso-bidi-font-weight:bold'><span style=3D'mso-spacerun:yes'>&nbsp; </span>t=
hat is
Ek is <o:p></o:p></span></h1>

<h1><span lang=3DEN-US style=3D'font-size:12.0pt;font-weight:normal;mso-bid=
i-font-weight:
bold'><span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp; </span>dive=
rgent
whiles </span><span lang=3DEN-US style=3D'font-size:12.0pt'>Yk(x)</span><sp=
an
lang=3DEN-US style=3D'font-size:12.0pt;font-weight:normal;mso-bidi-font-wei=
ght:
bold'> is convergent.<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp; </=
span><span
style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp; </span>(5CY)<o:p></o:p></span></h1>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<h1 align=3Dcenter style=3D'text-align:center'><span lang=3DEN-US><o:p>&nbs=
p;</o:p></span></h1>

<h1 align=3Dcenter style=3D'text-align:center'><span lang=3DEN-US>Expansion=
 of the
Particle</span><span lang=3DEN-US style=3D'font-size:14.0pt'><o:p></o:p></s=
pan></h1>

<h4><!--[if gte vml 1]><v:shape id=3D"_x0000_s1112" type=3D"#_x0000_t202" s=
tyle=3D'position:absolute;
 margin-left:306pt;margin-top:170.2pt;width:1in;height:198pt;z-index:-5'
 filled=3D"f" stroked=3D"f"/><![endif]--><![if !vml]><span style=3D'mso-ign=
ore:vglayout;
position:absolute;z-index:-5;margin-left:408px;margin-top:227px;width:100px;
height:268px'>

<table cellpadding=3D0 cellspacing=3D0>
 <tr>
  <td width=3D100 height=3D268 style=3D'vertical-align:top'><![endif]><![if=
 !mso]><span
  style=3D'position:absolute;mso-ignore:vglayout;z-index:-5'>
  <table cellpadding=3D0 cellspacing=3D0 width=3D"100%">
   <tr>
    <td><![endif]>
    <div v:shape=3D"_x0000_s1112" style=3D'padding:3.6pt 7.2pt 3.6pt 7.2pt'
    class=3Dshape>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt'>f</span><span lang=3D=
EN-US>
    &lt; </span><span lang=3DEN-US style=3D'font-size:22.0pt'>&#8734;<o:p><=
/o:p></span></h4>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso=
-bidi-font-weight:
    bold'>g</span><span lang=3DEN-US> &lt; </span><span lang=3DEN-US
    style=3D'font-size:22.0pt'>&#8734;<o:p></o:p></span></h4>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso=
-bidi-font-weight:
    bold'>e</span><span lang=3DEN-US> &lt; </span><span lang=3DEN-US
    style=3D'font-size:22.0pt'>&#8734;</span></h4>
    <h4><span lang=3DEN-US style=3D'font-size:22.0pt'><o:p>&nbsp;</o:p></sp=
an></h4>
    <h4><span lang=3DEN-US style=3D'font-size:22.0pt'><o:p>&nbsp;</o:p></sp=
an></h4>
    <h4><span lang=3DEN-US style=3D'font-size:22.0pt'><o:p>&nbsp;</o:p></sp=
an></h4>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso=
-bidi-font-weight:
    bold'>t</span><span lang=3DEN-US> &gt; </span><span lang=3DEN-US
    style=3D'font-size:18.0pt;font-weight:normal;mso-bidi-font-weight:bold'=
>0</span><span
    lang=3DEN-US style=3D'font-size:22.0pt'><o:p></o:p></span></h4>
    <h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso=
-bidi-font-weight:
    bold'>d</span><span lang=3DEN-US style=3D'font-family:Wingdings;mso-asc=
ii-font-family:
    "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:
    symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-char-type:s=
ymbol;
    mso-symbol-font-family:Wingdings'>&agrave;</span></span><span lang=3DEN=
-US> </span><span
    lang=3DEN-US style=3D'font-size:22.0pt'>0<o:p></o:p></span></h4>
    <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
    </div>
    <![if !mso]></td>
   </tr>
  </table>
  </span><![endif]><![if !mso & !vml]>&nbsp;<![endif]><![if !vml]></td>
 </tr>
</table>

</span><![endif]><span lang=3DEN-US><span style=3D'mso-no-proof:yes'><!--[i=
f gte vml 1]><v:shape
 id=3D"Picture_x0020_46" o:spid=3D"_x0000_i1036" type=3D"#_x0000_t75" style=
=3D'width:1in;
 height:58.5pt;visibility:visible'>
 <v:imagedata src=3D"reality_files/image016.emz" o:title=3D"" cropright=3D"=
35462f"/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D96 height=3D78
src=3D"reality_files/image017.gif" v:shapes=3D"Picture_x0020_46"><![endif]>=
</span><span
style=3D'mso-spacerun:yes'>&nbsp; </span></span><span lang=3DEN-US
style=3D'font-size:72.0pt;font-family:Wingdings;mso-ascii-font-family:"Time=
s New Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span><span
lang=3DEN-US><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span style=3D'mso-no-proof:yes'><!--[if gte vml 1]><v:shape id=3D"P=
icture_x0020_47"
 o:spid=3D"_x0000_i1037" type=3D"#_x0000_t75" style=3D'width:162pt;height:1=
43.25pt;
 visibility:visible'>
 <v:imagedata src=3D"reality_files/image014.emz" o:title=3D"" cropright=3D"=
36167f"/>
</v:shape><![endif]--><![if !vml]><img border=3D0 width=3D216 height=3D191
src=3D"reality_files/image015.gif" v:shapes=3D"Picture_x0020_47"><![endif]>=
</span></span></h4>

<h4><span lang=3DEN-US style=3D'font-size:18.0pt'>f</span><span lang=3DEN-U=
S> </span><span
lang=3DEN-US style=3D'font-family:Wingdings;mso-ascii-font-family:"Times Ne=
w Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Wingdings'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Wingd=
ings'>&agrave;</span></span><span
lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-size:22.0pt'>&#8734;<=
o:p></o:p></span></h4>

<h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso-bid=
i-font-weight:
bold'>g</span><span lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-f=
amily:
Wingdings;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti=
mes New Roman";
mso-char-type:symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-c=
har-type:
symbol;mso-symbol-font-family:Wingdings'>&agrave;</span></span><span
lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-size:22.0pt'>&#8734;<=
o:p></o:p></span></h4>

<h4><span lang=3DEN-US style=3D'font-size:18.0pt;font-weight:normal;mso-bid=
i-font-weight:
bold'>e</span><span lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-f=
amily:
Wingdings;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Ti=
mes New Roman";
mso-char-type:symbol;mso-symbol-font-family:Wingdings'><span style=3D'mso-c=
har-type:
symbol;mso-symbol-font-family:Wingdings'>&agrave;</span></span><span
lang=3DEN-US> </span><span lang=3DEN-US style=3D'font-size:22.0pt'>&#8734;<=
o:p></o:p></span></h4>

<h4 align=3Dcenter style=3D'text-align:center'><span lang=3DEN-US style=3D'=
font-size:
14.0pt'>Fig 1.5.1 f is frequency, g is mass, e is energy<o:p></o:p></span><=
/h4>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'>The following=
 laws
govern expansion quantum expansion<o:p></o:p></b></p>

<p class=3DMsoNormal><b style=3D'mso-bidi-font-weight:normal'><o:p>&nbsp;</=
o:p></b></p>

<p class=3DMsoNormal><span style=3D'mso-spacerun:yes'>&nbsp;</span>(1) <b
style=3D'mso-bidi-font-weight:normal'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;</span>Energy density En</b>, varies
inversely as Pn(x).<span style=3D'mso-spacerun:yes'>&nbsp; </span><span
style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>(2E)<b
style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:14.0pt'><o:p=
></o:p></span></b></p>

<p class=3DMsoNormal><span style=3D'mso-spacerun:yes'>&nbsp;</span>(2)<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span><b style=3D'mso-bidi-font-we=
ight:
normal'>Pn(x)</b> is uniform and divergent with respect to n. <span
style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
p;&nbsp;&nbsp;&nbsp;&nbsp; </span>(4E)
</p>

<p class=3DMsoNormal>(3)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </spa=
n><b
style=3D'mso-bidi-font-weight:normal'>Yn(x)</b> is uniform and divergent wi=
th
respect to n. <span style=3D'mso-tab-count:3'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp=
;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&n=
bsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>(4EY)
</p>

<p class=3DMsoNormal>(4)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </spa=
n>For
any two given integers k, j where k&gt;j the Schrodinger </p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n>wave
function gives Pk(x)&gt;Pj(x), and Ek&lt;Ej<span
style=3D'mso-spacerun:yes'>&nbsp; </span>that is Ek is </p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>convergent whiles Pk(x) is divergent.<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;
</span><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp; </span>(5E)</p>

<p class=3DMsoNormal>(5)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </spa=
n>For
any two given integers k, j where k&gt;j the Schrodinger </p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n>wave
function gives Yk(x)&gt;Yj(x), and Ek&lt;Ej<span
style=3D'mso-spacerun:yes'>&nbsp; </span>that is Ek is </p>

<p class=3DMsoNormal><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>convergent whiles Yk(x) is divergent.<span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;
</span><span style=3D'mso-tab-count:4'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nb=
sp;&nbsp; </span>(5EY)</p>

<p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font=
-weight:
normal'><span style=3D'mso-spacerun:yes'>&nbsp;</span><o:p></o:p></b></p>

<p class=3DMsoNormal><span style=3D'font-size:13.5pt;font-family:"new centu=
ry schoolbook"'><o:p>&nbsp;</o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'>=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D<o:p></o:p></span></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

<p class=3DMsoNormal><span style=3D'font-size:18.0pt'><o:p>&nbsp;</o:p></sp=
an></p>

</div>

</body>

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