Time-Independent Perturbation Theory

Abstract

A particle of mass m is constrained to move along an L length segment in the presence of a small potential well, so that the total potential is

$$V(x)={\left\{ \begin{array}{ll} \infty ,&{}\text {if } x< 0\,\, \text {and }x > L,\\ -V_0 ,&{}\text {if } 0< x< \frac{L}{2},\\ 0 &{}\text {if } \frac{L}{2}<x<L. \end{array}\right. } $$

Consider the small potential well (see Fig. 6.1) between 0 and $\frac{L}{2}$ as a perturbation compared to the infinite confining well and calculate the energy eigenvalues at the first perturbative order.