Quantum Mechanics: Concepts and Applications · Problem 5.1

Angular Momentum — Nouredine Zettili

Physics — Quantum Mechanics · orbital-angular-momentum-commutators

Problem

(a) Calculate the commutators [X^,L^x][\hat{X}, \hat{L}_x], [X^,L^y][\hat{X}, \hat{L}_y], and [X^,L^z][\hat{X}, \hat{L}_z]. (b) Calculate the commutators: [P^x,L^x][\hat{P}_x, \hat{L}_x], [P^x,L^y][\hat{P}_x, \hat{L}_y], and [P^x,L^z][\hat{P}_x, \hat{L}_z]. (c) Use the results of (a) and (b) to calculate [X^,L^2][\hat{X}, \hat{L}^2] and [P^x,L^2][\hat{P}_x, \hat{L}^2].

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