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This is the code we rely on to create a three dimensional plot in position or energy space with the complex plane in order to visualize time evolution. We’ve set the scale, ${s}$, the fraction of eigenvalue axis that is displayed, as an input as well in order to better scale the plots in both position space and energy space.

Code for Three Dimensional Plot of TDSE

function AW_plot3(basisaxis,psi,s);
%% Plot complex valued vectors as 3D plots. The complex plane forms the
%% backdrop for the plot and the eigenvalue axis (defining the space)
%% projects out from that plane.
        
        % s = 1; % 1/s defines the fraction of eigenvalue axis that is displayed
        
    % Begin by grabbing the real and imaginary parts of the vector psi,
    % defining the length of the "space" axis, and defining a vector of 
    % zeros that serve as the axis relative to which psi is plotted.
        realpart = real(psi);   % extract the real part of psi
        imagpart = imag(psi);   % extract the imaginary part of psi
        n = length(basisaxis);  % number of points in each vector
        bsl = zeros(n,1);       % define baseline as n zeros

    % Create a three dimensional stem plot. The bases of the stems are 
    % placed at the baseline "bsl" and the heads of the stems are displaced
    % from the baseline by the real and imaginary values of each vector
    % element
        plot3(...
          [basisaxis basisaxis]',[bsl realpart]',[bsl imagpart]','k',... % draw black stems
          basisaxis,realpart,imagpart,'b.') % draw stem heads as blue dots
        axis([min(basisaxis) max(basisaxis)/s -1 1  -1 1]); % set axis limits
        pbaspect([3,1,1])   % fix aspect ratio of 3D plot
        view([70,10])       % define the view angle
        grid on             % turn on the grid


end