
#1
Dec1712, 02:59 PM

P: 79

I havn't had much classes on numerical methods in quantum mechanics and I'm wondering how one would solve a general problem involving 2d motion. With general, I mean a problem that cannot be separated. Consider for instance the hamiltonian
[itex]\hat{H} = \frac{\widehat{p}_{x}^{2}+\widehat{p}_{y}^{2}}{2m}+x^{2}y^{2}[/itex] How does one find the eigenvalues and eigen functions numerically? 



#2
Dec1812, 09:21 AM

Sci Advisor
P: 3,375

1. Use a basis of e.g. harmonic oscillator eigenfunctions and a diagonalization routine for symmetric matrices (e.g. Lapack).
2. Use a grid of points and finite difference approximation for the derivatives. Then diagonalize the matrix like in 1. 


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