Time-independent 2D Schrodinger equation with non separable potential

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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

Answers (3)

Raul Lozano
Raul Lozano on 8 May 2013
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.

Zhaorong Wang
Zhaorong Wang on 27 Aug 2015

Laurent NEVOU
Laurent NEVOU on 15 Jan 2018
Look here:
https://github.com/LaurentNevou/Schrodinger2D_demo

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