Solving Time-independent 2D Schrodinger equation with finite difference method

Hi, I need to solve a 2D time-independent Schrodinger equation using Finite Difference Method(FDM). The potential is assumed to be 0 throughout and I am using standard five point finite difference discretization scheme. My grid size in two directions x and y (say Nx & Ny) is rather large, Nx=Ny=160.

So the size of the FDM matrix is (25600,25600) though it is sparse. I need only smallest 15-20 eigenvalues and corresponding eigenvectors.

Can someone suggest how to get the eigenvalues without dealing with the entire matrix which will obviously cause memory issues. Will SVD help?

PS: I am going through the methods to store large sparse matrices, any suggestions on storing the matrix elements will be greatly appreciated.

Thanks and Regards, Dibakar

Answer 1

[Milos Dubajic]

You can use spdiags to create sparse matrices which will help you to save memory.

Answer 2

[John D'Errico]

Just use the tool designed to solve your problem.

help eigs

Answer 3

[Laurent NEVOU]

Look at this example: https://github.com/LaurentNevou/Schrodinger2D_demo