Question

difference between non degenarate and degenerate time independent perturbation theory??

Answer 1

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Answer 2

Degeneracy vs. Non-Degeneracy

Recall that degeneracy in quantum mechanics refers to the situation when more than one eigenstate corresponds to the same energy. Conversely, non-degeneracy occurs when each eigenstate corresponds to a unique energy. Take for example,the hydrogen atom: in the absence of any external field, and ignoring spin, an electron in the nthenergy level can have orbital quantum numbers

and magnetic quantum numbers

Each combination of these quantum numbers corresponds to a particular eigenstate, but all of these eigenstates correspond to the same energy. However, in the presence of an external field, each of these eigenstates would correspond to a unique energy--the degeneracy is removed.

In non-degenerate perturbation theory there is no degeneracy of eigenstates; each eigenstate corresponds to a unique eigenenergy. One must only be concerned with the slight effects of the perturbing potential on the eigenenergies and eigenstates. However, the situation is not so simple in degenerate perturbation theory: the perturbing potential removes the degeneracy and alters the individual eigenstates.