# 1st order Pertubation energy and wavefunction

1. Nov 26, 2011

### 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:

$\leftψn0\langle$ H'$\rightψn0\rangle$

Where:
ψn0
Is the solution of the unpertubated Hamiltonian.

My question is can ψn0 be the general solution to the Hamiltonian or has to be a specified state vector?

i.e.,

ψn0= aψ10+bψ20

Or has to be:

ψn010

If it can be the superposition of the eigenstates, then how to construct the first order wave function?

2. Nov 26, 2011

### dextercioby

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

3. Nov 27, 2011

### luxiaolei

Thank you so much!