First order correction of wavefunction in degenerate perturbation

[zhanhai]

In first order correction of wavefunction,

|ψ⁽¹⁾_n>=∑ψ⁽⁰⁾_m<ψ⁽⁰⁾_m|V|ψ⁽⁰⁾_n>/(E⁽⁰⁾_n−E⁽⁰⁾_m)

when any two of the original states degenerate, we replace the two states with their corresponding "good states" to get a new set of "undisturbed" states (ψ⁽⁰⁾_m), AND then we determine the first order correction of each of the "good states" using the above expression with respect to the new set of "undisturbed" states. Is this understanding correct?

(I have read through several textbooks for this, and have found no clear description.)

 

[DrClaude]

In first order correction of wavefunction,

|ψ⁽¹⁾_n>=∑ψ⁽⁰⁾_m<ψ⁽⁰⁾_m|V|ψ⁽⁰⁾_n>/(E⁽⁰⁾_n−E⁽⁰⁾_m)

when any two of the original states degenerate, we replace the two states with their corresponding "good states" to get a new set of "undisturbed" states (ψ⁽⁰⁾_m), AND then we determine the first order correction of each of the "good states" using the above expression with respect to the new set of "undisturbed" states. Is this understanding correct?

If by "good states" you mean the linear combinations obtained from the secluar equations after solving for $E^{(1)}$, then yes, that is correct.