jcwojdel / quantum_talk Goto Github PK

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         sodipodi:role="line"
         id="tspan20557-8">Chemists version of Schroedinger's equation</tspan><tspan
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         y="868.8125"
         x="180.36375"
         sodipodi:role="line"
         id="tspan21941">(thanks to Born and Oppenheimer, mostly)</tspan><tspan
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         y="884.43536"
         x="180.36375"
         sodipodi:role="line"
         id="tspan21966">- No time</tspan><tspan
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         y="900.05817"
         x="180.36375"
         sodipodi:role="line"
         id="tspan21968">- No imaginary numbers</tspan><tspan
         style="font-size:12.49826241px"
         y="915.68103"
         x="180.36375"
         sodipodi:role="line"
         id="tspan21970">- Simple matrix diagonalisation problem</tspan></text>
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         sodipodi:role="line">This slide is</tspan><tspan
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         id="tspan27896"
         y="563.427"
         x="466.48303"
         sodipodi:role="line">ugly:</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:'Comic Sans MS';-inkscape-font-specification:'Comic Sans MS';fill:#505050;fill-opacity:1"
         y="584.23993"
         x="466.48303"
         sodipodi:role="line"
         id="tspan148560">it contains</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:'Comic Sans MS';-inkscape-font-specification:'Comic Sans MS';fill:#505050;fill-opacity:1"
         id="tspan27898"
         y="605.05292"
         x="466.48303"
         sodipodi:role="line">too much math</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:'Comic Sans MS';-inkscape-font-specification:'Comic Sans MS';fill:#505050;fill-opacity:1"
         id="tspan27900"
         y="625.86584"
         x="466.48303"
         sodipodi:role="line">and a cat</tspan><tspan
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         y="646.67877"
         x="466.48303"
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         y="667.4917"
         x="466.48303"
         sodipodi:role="line">Comic Sans)</tspan></text>
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       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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    <text
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       xml:space="preserve"
       style="font-style:normal;font-weight:normal;font-size:1.62130129px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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         style="font-size:9.9986105px">Cornelius Lanczos says:</tspan><tspan
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         style="font-size:9.9986105px">&quot;If you keep repeating the same operation</tspan><tspan
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         sodipodi:role="line"
         x="190.46581"
         y="985.35461"
         style="font-size:9.9986105px">over and over again, the result will finally be</tspan><tspan
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         y="997.85291"
         style="font-size:9.9986105px">what you want it to be (just bigger)&quot;</tspan></text>
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         sodipodi:role="line">Ax = λx</tspan></text>
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         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:'Comic Sans MS';-inkscape-font-specification:'Comic Sans MS';fill:url(#linearGradient148244);fill-opacity:1"
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         sodipodi:role="line">Dear agile coach: there is actual proof for that</tspan></text>
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       id="text30489"
       y="854.12433"
       x="485.03632"
       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
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   id="tspan30543"
   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080">    def</tspan> lanczos(<tspan
   id="tspan30593"
   style="font-style:italic">self</tspan>):</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#808080"
         id="tspan30493"
         y="866.62433"
         x="485.03632"
         sodipodi:role="line">        # Loop long enough,</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30495"
         y="879.12433"
         x="485.03632"
         sodipodi:role="line"><tspan
   id="tspan30545"
   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080">        for</tspan> _ <tspan
   id="tspan30547"
   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080">in</tspan> range(<tspan
   id="tspan30615"
   style="fill:#800000">40000</tspan>):</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#808080"
         id="tspan30497"
         y="891.62433"
         x="485.03632"
         sodipodi:role="line">            # Just apply Hessian operator for a given potential</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30499"
         y="904.12433"
         x="485.03632"
         sodipodi:role="line">            new_wf = <tspan
   id="tspan30595"
   style="font-style:italic">self</tspan>.wavefunction.hessian(<tspan
   id="tspan30599"
   style="font-style:italic">self</tspan>.potential)</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30501"
         y="916.62433"
         x="485.03632"
         sodipodi:role="line" /><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#808080"
         id="tspan30503"
         y="929.12433"
         x="485.03632"
         sodipodi:role="line">            # Orthogonalise with respect to previously found solutions</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30505"
         y="941.62433"
         x="485.03632"
         sodipodi:role="line"><tspan
   id="tspan30549"
   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080">            for</tspan> old_wf <tspan
   id="tspan30551"
   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080">in</tspan><tspan
   id="tspan30597"
   style="font-style:italic"> self</tspan>.wf_list:</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30507"
         y="954.12433"
         x="485.03632"
         sodipodi:role="line">                new_wf.orthogonalize(old_wf)</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30509"
         y="966.62433"
         x="485.03632"
         sodipodi:role="line" /><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#666666"
         id="tspan30511"
         y="979.12433"
         x="485.03632"
         sodipodi:role="line">            # Figure out the proportionality constant (energy)</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30513"
         y="991.62433"
         x="485.03632"
         sodipodi:role="line"><tspan
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   style="font-style:italic">            self</tspan>.last_energy = <tspan
   id="tspan30603"
   style="font-style:italic">self</tspan>.wavefunction.projection(new_wf)</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30515"
         y="1004.1243"
         x="485.03632"
         sodipodi:role="line" /><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#666666"
         id="tspan30517"
         y="1016.6243"
         x="485.03632"
         sodipodi:role="line">            # Normalize the resulting wavefunction</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
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         x="485.03632"
         sodipodi:role="line">            new_wf.normalize()</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30521"
         y="1041.6243"
         x="485.03632"
         sodipodi:role="line" /><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#666666"
         id="tspan30523"
         y="1054.1243"
         x="485.03632"
         sodipodi:role="line">            # Check if we already converged</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
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         x="485.03632"
         sodipodi:role="line"><tspan
   id="tspan30553"
   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080">            if</tspan><tspan
   id="tspan30605"
   style="font-style:italic"> self</tspan>.wavefunction.difference(new_wf) &lt; <tspan
   id="tspan30617"
   style="fill:#800000">0.1</tspan>:</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080"
         id="tspan30527"
         y="1079.1243"
         x="485.03632"
         sodipodi:role="line">                break</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30529"
         y="1091.6243"
         x="485.03632"
         sodipodi:role="line" /><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace;fill:#666666"
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         y="1104.1243"
         x="485.03632"
         sodipodi:role="line">            # Store the new wavefunction and loop over</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
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         y="1116.6243"
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         sodipodi:role="line"><tspan
   id="tspan30607"
   style="font-style:italic">            self</tspan>.wavefunction = new_wf</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30535"
         y="1129.1243"
         x="485.03632"
         sodipodi:role="line" /><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
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   id="tspan30557"
   style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:monospace;-inkscape-font-specification:monospace;fill:#000080">        print</tspan>(<tspan
   id="tspan30619"
   style="fill:#008000">&quot;E:&quot;</tspan>, <tspan
   id="tspan30609"
   style="font-style:italic">self</tspan>.last_energy)</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30539"
         y="1154.1243"
         x="485.03632"
         sodipodi:role="line"><tspan
   id="tspan30613"
   style="font-style:italic">        self</tspan>.wf_list.append(<tspan
   id="tspan30611"
   style="font-style:italic">self</tspan>.wavefunction)</tspan><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         id="tspan30541"
         y="1166.6243"
         x="485.03632"
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    <text
       xml:space="preserve"
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         y="857.09387"
         id="tspan30789"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"><tspan
   id="tspan31549"
   style="fill:#000080">    def</tspan> laplacian(<tspan
   id="tspan31627"
   style="font-style:italic">self</tspan>):</tspan><tspan
         id="tspan31420"
         sodipodi:role="line"
         x="926.24951"
         y="869.59387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace">        result = numpy.zeros([<tspan
   id="tspan31583"
   style="font-style:italic">self</tspan>.BASE_SIZE])</tspan><tspan
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         sodipodi:role="line"
         x="926.24951"
         y="882.09387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace">        result[<tspan
   id="tspan31587"
   style="fill:#800000">0</tspan>] = <tspan
   id="tspan31585"
   style="fill:#800000">0.</tspan> + <tspan
   id="tspan31581"
   style="font-style:italic">self</tspan>._psi[<tspan
   id="tspan31615"
   style="fill:#800000">1</tspan>] - <tspan
   id="tspan31617"
   style="fill:#800000">2</tspan> * <tspan
   id="tspan31579"
   style="font-style:italic">self</tspan>._psi[<tspan
   id="tspan31619"
   style="fill:#800000">0</tspan>]</tspan><tspan
         id="tspan31424"
         sodipodi:role="line"
         x="926.24951"
         y="894.59387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace">        result[<tspan
   id="tspan31589"
   style="fill:#800000">-1</tspan>] = <tspan
   id="tspan31569"
   style="font-style:italic">self</tspan>._psi[<tspan
   id="tspan31613"
   style="fill:#800000">-2</tspan>] + <tspan
   id="tspan31611"
   style="fill:#800000">0.0</tspan> - <tspan
   id="tspan31609"
   style="fill:#800000">2</tspan> * <tspan
   id="tspan31577"
   style="font-style:italic">self</tspan>._psi[<tspan
   id="tspan31607"
   style="fill:#800000">-1</tspan>]</tspan><tspan
         id="tspan31426"
         sodipodi:role="line"
         x="926.24951"
         y="907.09387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace">        result[<tspan
   id="tspan31591"
   style="fill:#800000">1</tspan>:<tspan
   id="tspan31593"
   style="fill:#800000">-1</tspan>] = <tspan
   id="tspan31567"
   style="font-style:italic">self</tspan>._psi[<tspan
   id="tspan31595"
   style="fill:#800000">0</tspan>:<tspan
   id="tspan31597"
   style="fill:#800000">-2</tspan>] + <tspan
   id="tspan31573"
   style="font-style:italic">self</tspan>._psi[<tspan
   id="tspan31599"
   style="fill:#800000">2</tspan>:] - <tspan
   id="tspan31601"
   style="fill:#800000">2</tspan> * <tspan
   id="tspan31575"
   style="font-style:italic">self</tspan>._psi[<tspan
   id="tspan31603"
   style="fill:#800000">1</tspan>:<tspan
   id="tspan31605"
   style="fill:#800000">-1</tspan>]</tspan><tspan
         id="tspan31428"
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         x="926.24951"
         y="919.59387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"><tspan
   id="tspan31571"
   style="fill:#000080">        return</tspan> result</tspan><tspan
         id="tspan31430"
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         x="926.24951"
         y="932.09387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace" /><tspan
         id="tspan31432"
         sodipodi:role="line"
         x="926.24951"
         y="944.59387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"><tspan
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   style="fill:#000080">    def</tspan> hessian(<tspan
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         sodipodi:role="line"
         x="926.24951"
         y="957.09387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace">        laplacian = <tspan
   id="tspan31565"
   style="font-style:italic">self</tspan>.laplacian()</tspan><tspan
         id="tspan31436"
         sodipodi:role="line"
         x="926.24951"
         y="969.59387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace" /><tspan
         id="tspan31438"
         sodipodi:role="line"
         x="926.24951"
         y="982.09387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace">        new_wf = GridWavefunction1D(-laplacian + potential.operate(<tspan
   id="tspan31625"
   style="font-style:italic">self</tspan>))</tspan><tspan
         id="tspan31440"
         sodipodi:role="line"
         x="926.24951"
         y="994.59387"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"><tspan
   id="tspan31553"
   style="fill:#000080">        return</tspan> new_wf</tspan></text>
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       id="text31442"
       y="1140.4297"
       x="927.79999"
       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
       xml:space="preserve"><tspan
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:monospace;-inkscape-font-specification:monospace"
         y="1140.4297"
         x="927.79999"
         sodipodi:role="line"
         id="tspan31466"><tspan
   id="tspan31555"
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         style="font-size:15px">https://github.com/jcwojdel/quantum_talk</tspan></text>
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