Franz Schwabl Quantum Mechanics 4th Edit · Problem 2.4

One-Dimensional Problems

Physics — Quantum Mechanics · hermitian-operators-commutators

Problem

Show that (a)

p^\dagger = p

(p^2)^\dagger = p^2

V(\boldsymbol{x})^\dagger = V(\boldsymbol{x})

(b)

(AB)^\dagger = B^\dagger A^\dagger

(c)

[AB, C] = A[B,C] + [A,C]B