Calculating the Energy Spectrum in a Hamiltonian: Tips and Techniques?

[babylonia]

Hi everyone,

I'm having some problems with this topic. how to numerically calculate the energy spectrum for a certain Hamiltonian? eg., in a periodic potential or disordered potential:
\widehat{H}=-\frac{\partial^{2}}{\partial x^{2}}+cos(x)+V(x)

Thanks for your time and attention.

 

[kanato]

Expand your wavefunction in a basis of differentiable functions, and then you will convert your differential equation into a matrix eigenvalue equation. From there, use any matrix eigenvalue routine to get your energy spectrum.

 

[babylonia]

Hi Kanato,

Thanks for reply.

Still I'm not clear with which basis it is appropriate to calculate the E(k) spectrum in disordered potential, since there may be a trucation problem in numerical implementation. Is there any special technique?

Best regards