Introduction to Quantum Mechanics · Problem 3.5

Formalism — David J. Griffiths

Physics — Quantum Mechanics · hermitian_conjugates

Problem

(a) Find the hermitian conjugates of

x

i

, and

d/dx

. (b) Show that

(\hat{Q}\hat{R})^\dagger = \hat{R}^\dagger\hat{Q}^\dagger

(note the reversed order),

(\hat{Q} + \hat{R})^\dagger = \hat{Q}^\dagger + \hat{R}^\dagger

, and

(c\hat{Q})^\dagger = c^*\hat{Q}^\dagger

for a complex number

c

. (c) Construct the hermitian conjugate of

a_+

(Equation 2.48).