1st order Pertubation energy and wavefunction

[luxiaolei]

Hi all,

I must misunderstood somewhere, couldn't figure out the following, any helps will be greatly appreciated.

The first order correction of the pertubated energy is:

$\leftψ_n⁰\langle$ H^'$\rightψ_n⁰\rangle$

Where:
ψ_n⁰
Is the solution of the unpertubated Hamiltonian.

My question is can ψ_n⁰ be the general solution to the Hamiltonian or has to be a specified state vector?

i.e.,

ψ_n⁰= aψ₁⁰+bψ₂⁰

Or has to be:

ψ_n⁰=ψ₁⁰

If it can be the superposition of the eigenstates, then how to construct the first order wave function?
Thanks in advance:)

 

[dextercioby]

The correction is calculated for a particular eigenvector of the Hamiltonian and not for a superposition of several eigenvectors.

 

[luxiaolei]

The correction is calculated for a particular eigenvector of the Hamiltonian and not for a superposition of several eigenvectors.

Thank you so much!