Question

(a) Show that eipα/ℏx e−i pα/ℏ = x + α

(b) If A and B are Hermitian, find the condition that the product AB will be Hermitian

Answer 1

(b) If A and B are Hermitian

(AB)† = B†A† = B A

If the product is to be Hermitian then (AB) † = AB i.e. AB = B A. Thus, A and B must commute with each other.