Where can I find perturbation theory formulas up to fourth order?

[jeffreydk]

Does anybody happen to know where to find the perturbation theory formulas for the energies and states up to fourth order? I have to do a calculation up to this order and don't want to have to derive them if I don't have to (I know that Wikipedia has high order energies, but they only have the states up to second order).

Thanks very much for your help.

 

[Matterwave]

Well, my QM book recommends for fourth and fifth order: Niholas Wheeler's Higher-Order Spectral Perturbation. I haven't read this myself so I'm not sure what exactly is in there...

As far as I know, this is also just for non-degenerate perturbation theory.

 

[jeffreydk]

Thank you very much for the suggestion. I am working with a non-degenerate case so I'll take a look.

 

[SpectraCat]

In my own experience, when it becomes necessary to go beyond 2nd order PT, I generally just set up the variational matrix (in the basis of unperturbed states) and diagonalize it ... that gets all (or at least many) of the higher order PT terms in there implicitly. I don't know if that would be workable for you, but it is probably not any more work than working out the fourth order PT terms ...