Register to reply 
How to solve 2d problems numerically. 
Share this thread: 
#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: 3,633

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 