Define the displacement operator D(z) by (a) Show that D(z) is unitary. (b) Show that the coherent state  (You will need to use the Baker–Campbell– Hausdorff identity from Problem 5.8.) (c) Evaluate...

Define the displacement operator D(z) by

(a) Show that D(z) is unitary.

(b) Show that the coherent state
 (You will need to use the Baker–Campbell– Hausdorff identity from Problem 5.8.)

(c) Evaluate D(z)|zfor the coherent state |z.

This version of the displacement operator has somewhat more elegant properties than the simpler one mentioned in Exercise 13.24.