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      <p bold="true">Two-dimensional Fourier momentum </p>
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    <writer lang="eng"><![CDATA[<span style="font-family: 'Arial'; font-size: 10pt; font-weight: normal; font-style: normal; color: Black; background-color: Transparent; text-align: left; line-height: 115%">
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 14pt"><strong><span style="color: Blue">Fourier Quantum</span></strong></span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt">Adapted from Mathcad 11, <strong><span style="color: Red">mathengjmg</span></strong> [web site].</span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt">Written permission from <strong><span style="color: #993366">Frank Rioux.</span></strong></span></span></div>
<div><a href="http://www.users.csbsju.edu/~frioux/workinprogress.html"><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt"><span style="text-decoration: underline"><span style="color: DarkBlue">http://www.users.csbsju.edu/~frioux/workinprogress.html</span></span></span></span></a></div></span>]]></writer>
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        <e type="operand">0.125</e>
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        <p>You need that one for scaling grayscale image</p>
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        <p>'R' hole positions</p>
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        <p>'r' hole positions</p>
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        <p>coordinate-space wave fnct</p>
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        <p>Fourier integral transform from wave function into momentum</p>
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        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">b</e>
        <e type="operand">x</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">c</e>
        <e type="operand">y</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">d</e>
        <e type="operand">y</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">1</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
      </input>
    </math>
  </region>
  <region id="10" left="18" top="828" width="740" height="76" color="#000000" bgColor="#ebebeb" fontSize="8">
    <math decimalPlaces="4">
      <description active="true" position="Top" lang="eng">
        <p>Optimiz =&gt; SYMBOLIC ... a bit faster</p>
      </description>
      <input>
        <e type="operand">px</e>
        <e type="operand">py</e>
        <e type="function" args="2">Ψ</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">d</e>
        <e type="operator" args="2">*</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operand">i</e>
        <e type="operand">x</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">px</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">exp</e>
        <e type="operand">i</e>
        <e type="operand">x</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">px</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">exp</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">i</e>
        <e type="operand">y</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">py</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">exp</e>
        <e type="operator" args="1">-</e>
        <e type="operand">i</e>
        <e type="operand">y</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">d</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">py</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">exp</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">px</e>
        <e type="operand">py</e>
        <e type="operator" args="2">*</e>
        <e type="operand">10</e>
        <e type="operand">12</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">m</e>
        <e type="operand">1</e>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="11" left="9" top="1035" width="96" height="26" color="#000000" bgColor="#ffff80" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">t0</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="12" left="9" top="1062" width="301" height="100" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <description active="true" position="Top" lang="eng">
        <p>Optimiz =&gt; Numeric</p>
      </description>
      <input>
        <e type="operand">Ω</e>
        <e type="operand">m</e>
        <e type="operand">1</e>
        <e type="operand">N</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operand">N</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">Fo</e>
        <e type="operand">m</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="operand">px</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">py</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="2">Ψ</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">Fo</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="13" left="315" top="1089" width="174" height="47" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math>
      <input>
        <e type="operand">Ω</e>
        <e type="operand">Ω</e>
        <e type="operator" args="2">:</e>
        <e type="operand">C</e>
        <e type="operand">Ω</e>
        <e type="operand">0</e>
        <e type="operand">255</e>
        <e type="function" args="3">Scale</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </math>
  </region>
  <region id="14" left="315" top="1134" width="231" height="99" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="operand">0.125</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
        <e type="operand">fmap</e>
        <e type="operand">Ω</e>
        <e type="function" args="1">f</e>
        <e type="function" preserve="true" args="1">vectorize</e>
        <e type="operator" args="2">:</e>
        <e type="operand">fmap</e>
        <e type="operand">fmap</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">255</e>
        <e type="function" args="3">Scale</e>
        <e type="operator" args="2">:</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">line</e>
      </input>
    </math>
  </region>
  <region id="15" left="549" top="1134" width="222" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="23.2251544198879" scale_y="4.52546060116815" scale_z="105.104521283249" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-57" transpose_y="-51" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
      </input>
    </plot>
  </region>
  <region id="16" left="36" top="1197" width="171" height="26" color="#000000" bgColor="#ffff80" fontSize="10">
    <math decimalPlaces="1">
      <input>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operand">t0</e>
        <e type="operator" args="2">-</e>
      </input>
      <contract>
        <e type="operand" style="unit">min</e>
      </contract>
      <result action="numeric">
        <e type="operand">31.4</e>
      </result>
    </math>
  </region>
  <region id="17" left="36" top="1242" width="110" height="108" color="#000000" bgColor="#ffffff" fontSize="10">
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      <description active="true" position="Right" lang="eng">
        <p>Mathcad 11'N' 100</p>
      </description>
      <input>
        <e type="operand">α</e>
        <e type="operand">image</e>
        <e type="operator" args="2">*</e>
      </input>
    </image>
  </region>
  <region id="20" left="18" top="1368" width="274" height="56" border="true" color="#000000" bgColor="#ffffe1" fontSize="10">
    <text lang="eng">
      <p>set N=101, export 'C' in your SmathFile, read back 'image' in blank work sheet, experiment 'α'</p>
    </text>
  </region>
</regions>