Chapter 12, Problem 12.65E

Interpretation Introduction

Interpretation:

The value of $\langle E^{\left(1\right)}\rangle$ is to be numerically evaluated. The agreement between the corresponding calculated value and the given value of the energy correction is to be demonstrated.

Concept introduction:

Perturbation theory assumes that a system can be approximated as a known, solvable system. The difference between the known system and system of interest is small and additive. The average value of observable energy is represented as,

$\langle E\rangle =\langle E^{\left(0\right)}\rangle +\langle E^{\left(1\right)}\rangle$

Where,

• $\langle E^{\left(0\right)}\rangle$ represents the average energy of the ideal system.

• $\langle E^{\left(1\right)}\rangle$ represents the first-order correction to the energy.