Chapter 40, Problem 40.34E

To determine

To show: The wave function $\psi \left(x\right)=C{e}^{-\frac{\sqrt{m{k}^{\prime }}{x}^2}{2\hslash }}$ is a solution to the one dimensional Schrodinger equation $-\frac{{\hslash }^2}{2m}\frac{d^2\psi \left(x\right)}{d{x}^2}+\frac{1}{2}{k}^{\prime }{x}^2\psi \left(x\right)=E\psi \left(x\right)$ for harmonic oscillator.