Chapter 10, Problem 10.41E

Verify that the following wavefunctions are indeed eigenfunctions of the Schrödinger equation, and determine their energy eigenvalues.

(a) $\Psi =e^{iKx}$ where $V=0$ and $K$ is a constant

(b) $\Psi =e^{iKx}$ where $V=k$, $k$ is some constant potential energy, and $K$ is a constant

(c) $\Psi =\sqrt{\frac{2}{a}}\sin \frac{\pi x}{a}$ where $V=0$.