A Modern Approach to Quantum Mechanics · Problem 6.8
The One-Dimensional Harmonic Oscillator — John S. Townsend
Physics — Quantum Mechanics · hermitian-operators
Problem
Establish that the position operator x^ is Hermitian (a) by showing that
⟨φ∣x^∣ψ⟩=⟨ψ∣x^∣φ⟩∗
or (b) by taking the adjoint of the position-momentum commutation relation (6.31).