Quantum Mechanics: Concepts and Applications · Problem 5.11

Three-Dimensional Problems — Nouredine Zettili

Physics — Quantum Mechanics · commutation-relations-operators

Problem

Using

[\hat{X},\ \hat{P}] = i\hbar

, calculate the various commutation relations between the following operators

\hat{T}_1 = \frac{1}{4}(\hat{P}^2 - \hat{X}^2), \qquad \hat{T}_2 = \frac{1}{4}(\hat{X}\hat{P} + \hat{P}\hat{X}), \qquad \hat{T}_3 = \frac{1}{4}(\hat{P}^2 + \hat{X}^2).