How Does a Perturbation Affect Energy in a Quantum Box?

[Demon117]

1. Calculate the first-order correction to E^{3}_{(0)} for a particle in a one-dimensional box with walls at x = 0 and x = a due to the following perturbations:

(a) H' = 10^{-3}E_{1}x/a
(b) H' = 10^{-3}E_{1}sin(x/a)

The Attempt at a Solution

The only attempt that I have made is to start with the equation E_{n}=E^{(0)}_{n}+H'_{nn}. But I have not really gotten anywhere with it. Does anyone have any ideas where to start with this question?

 

[vela]

The first-order correction to the energy of state |n\rangle is H'_nn, which is the matrix element \langle n|H'|n \rangle. You just need to calculate that for the given state and perturbations.

 

[Demon117]

The first-order correction to the energy of state |n\rangle is H'_nn, which is the matrix element \langle n|H'|n \rangle. You just need to calculate that for the given state and perturbations.

That is actually very helpful, thank you so much!