<?xml version="1.0" encoding="UTF-8"?> <simulation xmds-version="2"> <name>hermitegauss_transform</name> <author>Graham Dennis</author> <description> Solve the Schroedinger equation using the hermite-Gauss basis. </description> <features> <benchmark /> <!-- <error_check /> --> <bing /> <globals> <![CDATA[ const real offset = 1.0; ]]> </globals> </features> <geometry> <propagation_dimension> t </propagation_dimension> <transverse_dimensions> <dimension name="x" lattice="30" spectral_lattice="20" length_scale="1.0" transform="hermite-gauss" /> </transverse_dimensions> </geometry> <vector name="main" initial_basis="x" type="complex"> <components> psi </components> <initialisation> <![CDATA[ psi = pow(M_PI, -0.25) * exp(-0.25*(x - offset)*(x - offset)); ]]> </initialisation> </vector> <sequence> <integrate algorithm="RK4" tolerance="1e-6" interval="10." steps="100"> <samples>100 100 100</samples> <operators> <operator kind="ip" basis="nx"> <operator_names>L</operator_names> <![CDATA[ L = -i*(nx + 0.5); ]]> </operator> <integration_vectors>main</integration_vectors> <![CDATA[ dpsi_dt = L[psi]; ]]> </operators> </integrate> </sequence> <output> <sampling_group basis="x" initial_sample="no"> <moments>dens</moments> <dependencies>main</dependencies> <![CDATA[ dens = mod2(psi); ]]> </sampling_group> <sampling_group basis="nx" initial_sample="no"> <moments>dens</moments> <dependencies>main</dependencies> <![CDATA[ dens = mod2(psi); ]]> </sampling_group> <sampling_group basis="kx" initial_sample="no"> <moments>dens</moments> <dependencies>main</dependencies> <![CDATA[ dens = mod2(psi); ]]> </sampling_group> </output> </simulation>