Whole setup of perturbation theory is that we assume that we can taylor expand new perturbed energies and states (corresponding to perturbed hamiltionian) and then we can callculate terms sitting next to lambda (parameter that was introduced in the beggining of the theory), which are the corrections for the perturbed hamiltonian. 'First order shift' is simply the term sitting next to lambda^1 in the expansion. So what does it mean that the shift is valid even when degeneracy is not lifted, it simply means that we calculated all of corrections/terms sitting next to lamda^1 and we found out that they are same for different degenerate states, but this doesn`t mean that these corrections are wrong, it simply means that we are still not able to tell apart degenerate states with corrections that correspond to lambda^1.
12:20 I had exactly the same feeling ...
What does it mean by "first order shifts are valid even if the degeneracy is not lifted" in 8:51?
Whole setup of perturbation theory is that we assume that we can taylor expand new perturbed energies and states (corresponding to perturbed hamiltionian) and then we can callculate terms sitting next to lambda (parameter that was introduced in the beggining of the theory), which are the corrections for the perturbed hamiltonian. 'First order shift' is simply the term sitting next to lambda^1 in the expansion. So what does it mean that the shift is valid even when degeneracy is not lifted, it simply means that we calculated all of corrections/terms sitting next to lamda^1 and we found out that they are same for different degenerate states, but this doesn`t mean that these corrections are wrong, it simply means that we are still not able to tell apart degenerate states with corrections that correspond to lambda^1.
@@matusliptak9511 ah wow. Thanks for the comprehensive explanation
11:55