Consider a particle of energy (E) moving in a one-dimensional potential well (V(q)), such that [ m

Question:

Consider a particle of energy $E$ moving in a one-dimensional potential well $V(q)$, such that

\[
m \hbar\left|\frac{d V}{d q}ight| \ll\{m(E-V)\}^{3 / 2}
\]

Show that the allowed values of the momentum $p$ of the particle are such that

\[
\oint p d q=\left(n+\frac{1}{2}ight) h
\]

where $n$ is an integer.