Chapter 6.6, Problem 6.18P

(a)

To determine

Prove that the translation and inversion do not commute.

(b)

To determine

Show that the Eigen state of momentum and its parity are the same energy.

(c)

To determine

Show that the translation operator mixes $\frac{1}{\sqrt{\pi \hslash }}\cos \left(\frac{px}{\hslash }\right)$ and $\frac{1}{\sqrt{\pi \hslash }}\sin \left(\frac{px}{\hslash }\right)$ must be degenerate.