Parity (10 min)

Show that the solutions of the stationary Schrödinger equation with the one-dimensional potential

$$V(x)=\left\{ \begin{array}{cc} 0, & -\infty<x\le -a \\ -V<0, & -a <x\le a \\ 0 & a < x < \infty \end{array} \right.$$ (13)

can be chosen as even and odd solutions.