Chapter 10, Problem 10.11E

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

(a) $\frac{d}{dx}\cos 4x$ (b) $\frac{d^2}{d{x}^2}\cos 4\pi x$

(c) $\widehat{p_x}\left(\sin \frac{2\pi x}{3}\right)$ (d) $\hat{x}\left(\sqrt{\frac{2}{a}}\sin \frac{2\pi x}{a}\right)$

(e) $\hat{3}\left(4\ln x^2\right)$, where $\hat{3}=3\times$ (f) $\frac{d}{d\theta }\sin \pi \cos \theta$

(g) $\frac{d^2}{d{\theta }^2}\sin \pi \cos \theta$ (h) $\frac{d}{d\pi }\tan \pi$