Time-independent 2D Schrodinger equation with non separable potential

I would like to solve the time-independent 2D Schrodinger equation for a non separable potential using exact diagonalization. I understand I need to rewrite the problem so that the wavefunction which is a 2xN matrix is a 1xN² matrix so that the problem reduces to the diagonalization of a N²xN² hamiltonian. My question is : how should I use the meshgrid and del2 functions to define the laplacian part of the hamiltonian, and how should I write the matrix potential (say I have a function V(x, y) for the potential, how do I get the matrix potential in the rewritten problem ? And finally, how do get the eigenstates and eigenenergies of the initial problem ?

Thanks a lot

Answer 1

[Raul Lozano]

I would like to know this too. I see on Youtube that Greenville College has a project where they solve Schrodinger's equation using Wavelets. Your help with pointers to be able to do this with Matlab will greatly be appreciated.

Regards and thanks.

Answer 2

[Zhaorong Wang]

Take a look here, http://www.mathworks.com/matlabcentral/fileexchange/3344-2d-schroedinger-poisson-solver-aquila

Answer 3

[Laurent NEVOU]

Look here:

https://github.com/LaurentNevou/Schrodinger2D_demo