7.6 Exercise 21

Consider an infinite square well with wall boundaries $x = 0$ and $x = L .$ Show that the function $\psi \left(x\right) = A \text{sin} k x$ is the solution to the stationary Schrӧdinger equation for the particle in a box only if $k = \sqrt{2 m E} / \hbar .$ Explain why this is an acceptable wave function only if k is an integer multiple of $\pi / L .$