# Time independent perturbation theoery

Why do we talk of transitions only in time dependent perturbation theory when the eigen states are corrected even in time independent perturbation theory? If we can,for sake of argument,say : eigen states of the system in TIPT changes (get corrected) and so does state of the system before and after the perturbation ,from eigen state to another of the original Hamiltonian of the system in TDPT ,then why no transitions in latter .

With great care, I believe one can derive time independent perturbation theory from time dependent perturbation theory by considering a infinitely slowly varying perturbation. Starting at t=$-\infty$ with zero strength and reaching nominal strength at t=0. Infinitely slow perturbation keeps the system constantly in it's eigenstate, which was a ground state in this case. (See Gell-man and Low theorem) Only exception is that the perturbation changes the groundstate for example via un-avoided crossing of an excited state with a ground state (leading to a degenerate ground state). In other words, the system is perturbed adiabatically by keeping it constantly in its ground state. (Great care here excludes pathological cases such as degenerate ground state)