Textbook Problem

Indicate which of these expressions yield eigenvalue equations, and if so indicate the eigenvalue.

(a) $\frac{d}{dx}\sin \frac{\pi x}{2}$ (b) $\frac{d^2}{d{x}^2}\sin \frac{\pi x}{2}$

(c) $-i\hslash \frac{d}{dx}\sin \frac{\pi x}{2}$ (d) $-i\hslash \frac{d}{dx}{\text{e}}^{imx}$, where $m$ is a constant

(e) $\frac{d}{dx}\left({\text{e}}^x\right)$ (f) $\left(-\frac{{\hslash }^2}{2m}\frac{d^2}{d{x}^2}+0.5\right)\sin \frac{2\pi x}{3}$

(g) $\frac{d}{dy}\left({\text{e}}^{-y^2}\right)$