Chapter 12, Problem 12.37E

Interpretation Introduction

Interpretation:

The average energy of an electron in a ring having $m=1$ that experience a perturbation of $\widehat{H^{\prime }}=V\left(1-\sin 6\varphi \right)$ is to be calculated.

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. Thus, the Hamiltonian for the real system can be written as given below.

${\widehat{H}}_{\text{system}}={\widehat{H}}_{\text{ideal}}+{\widehat{H}}_{\text{perturb}}$