I want to develop a visual simulation of a propagating 2D wavefunction with an added attractive potential. Basically I have to numerically solve the time-dependent Schrodinger equation (PDE with x,y,t as variables) but, instead of boundary conditions, I want to have an incoming wavefunction of my choice as the initial wavefunction profile. What software would give me a good environment for such a project (I'm thinking Mathematica, Comsol, Matlab as a starting point)?
You could start from the step-23 or step-25 tutorial programs of deal.II, see for example http://www.dealii.org/7.2.0/doxygen/deal.II/step_23.html . (Disclaimer: I'm one of the authors of this library.)