Why are Diagonal Elements of a Time-Dependent Perturbed Hamiltonian Often Zero?

[Morten]

Why does a time-dependent perturbed Hamiltonian commonly have diagonal elements equal to zero?

 

[DrClaude]

Because the perturbation is what is going to mix the eigenstates of the unperturbed Hamiltonian. But the diagonal elements could be non-zero: an actual physical perturbation could also shift the energy levels. Most often, it is easier to work with a perturbation that only mixes the states, so I would move the diagonal elements to the "unperturbed" Hamiltonian in such a case.

 

[Morten]

Thanks!