<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>hermitegauss_transform_2d</name>
  <author>Graham Dennis</author>
  <description>
    Solve the Schroedinger equation using the hermite-Gauss basis.
  </description>
  
  <features>
    <benchmark />
    <!-- <error_check /> -->
    <bing />
    <validation kind="run-time" />
    <globals>
      <![CDATA[
        const real M = 9.1e-31; // Mass of an electron
        const real hbar = 1.05e-34;
        const real omega = 2*M_PI*1e3;
        const real offset = 1.0 * sqrt(hbar/(M*omega));
        
      ]]>
    </globals>
  </features>
  
  <geometry>
    <propagation_dimension> t </propagation_dimension>
    <transverse_dimensions>
      <dimension name="x" lattice="20" length_scale="sqrt(hbar/(M*omega))" transform="hermite-gauss" />
      <dimension name="y" lattice="20" length_scale="sqrt(hbar/(M*omega))" transform="hermite-gauss" />
    </transverse_dimensions>
  </geometry>
  
  <vector name="main" initial_basis="x y" type="complex">
    <components>
      psi
    </components>
    <initialisation>
      <![CDATA[
      psi = pow(M*omega/(hbar*M_PI), 0.25) * exp(-0.5*(M*omega/hbar)*(x - offset)*(x - offset));
      psi *= pow(M*omega/(hbar*M_PI), 0.25) * exp(-0.25*(M*omega/hbar)*y*y);
      ]]>
    </initialisation>
  </vector>
  
  <computed_vector name="normalisation" dimensions="" type="real">
    <components>N integral_y2</components>
    <evaluation>
      <dependencies>main</dependencies>
      <![CDATA[
        N = mod2(psi);
        integral_y2 = mod2(psi)*y*y;
      ]]>
    </evaluation>
  </computed_vector>
  
  <sequence>
    <integrate algorithm="ARK45" tolerance="1e-6" interval="1e-3" steps="400">
      <samples>10 1 100</samples>
      <operators>
        <operator kind="ip" basis="nx ny">
          <operator_names>L</operator_names>
          <![CDATA[
            L = -i*(nx + ny + 1.0)*omega;
          ]]>
        </operator>
        <integration_vectors>main</integration_vectors>
        <![CDATA[
          dpsi_dt = L[psi];
        ]]>
      </operators>
    </integrate>
  </sequence>
  <output>
      <sampling_group basis="x y" initial_sample="yes">
        <moments>dens</moments>
        <dependencies>main</dependencies>
        <![CDATA[
          dens = mod2(psi);
        
        ]]>
      </sampling_group>
      <sampling_group basis="nx ny" initial_sample="no">
        <moments>dens</moments>
        <dependencies>main</dependencies>
        <![CDATA[
          dens = mod2(psi);
        
        ]]>
      </sampling_group>
      <sampling_group basis="x(0) y(0)" initial_sample="yes">
        <moments>mean_x mean_sigmay</moments>
        <dependencies>main normalisation</dependencies>
        <![CDATA[
          mean_x = mod2(psi)*x/N;
          mean_sigmay = sqrt(integral_y2/N);
        ]]>
      </sampling_group>
  </output>
</simulation>