Chapter 40, Problem 50E

To determine

To show: The wave function $\psi \left(x\right)=A{e}^{ikx}$ is a solution to the one dimensional Schrodinger equation $-\frac{{\hslash }^2}{2m}\frac{d^2\psi \left(x\right)}{d{x}^2}+U\left(x\right)\psi \left(x\right)=E\psi \left(x\right)$. Determine the expression for $k$ and relate it with particles momentum and de Broglie wavelength.