A Modern Approach to Quantum Mechanics · Problem 9.8

Bound States of Central Potentials — John S. Townsend

Physics — Quantum Mechanics · angular-momentum-commutation-relations

Problem

Use the commutation relations [x^i,p^j]=iℏδij[\hat{x}_i, \hat{p}_j] = i\hbar\delta_{ij} to verify that the angular momentum operators L^=r^×p^\hat{\mathbf{L}} = \hat{\mathbf{r}} \times \hat{\mathbf{p}}, or, in component form, L^i=∑j=13∑k=13εijkx^jp^k\hat{L}_i = \sum_{j=1}^{3}\sum_{k=1}^{3} \varepsilon_{ijk}\hat{x}_j\hat{p}_k satisfy the commutation relations [L^i,L^j]=iℏ∑k=13εijkL^k[\hat{L}_i, \hat{L}_j] = i\hbar\sum_{k=1}^{3}\varepsilon_{ijk}\hat{L}_k

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