How to solve 2d problems numerically.


by ehj
Tags: numerically, solve
ehj
ehj is offline
#1
Dec17-12, 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?
Phys.Org News Partner Physics news on Phys.org
Researchers develop scalable methods for manufacturing metamaterials
Researchers find tin selenide shows promise for efficiently converting waste heat into electrical energy
After 13 years, progress in pitch-drop experiment (w/ video)
DrDu
DrDu is offline
#2
Dec18-12, 09:21 AM
Sci Advisor
P: 3,371
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.


Register to reply

Related Discussions
suggestions for scheme to use to solve PDE numerically Differential Equations 6
how to solve BdG Equations numerically Atomic, Solid State, Comp. Physics 0
To solve an equation numerically using mathematica. Math & Science Software 6
Is it possible to numerically solve this PDE? Differential Equations 0
Numerically Solve Math & Science Software 2