A Modern Approach to Quantum Mechanics · Problem 9.7

Translational and Rotational Symmetry in the Two-Body Problem — John S. Townsend

Physics — Quantum Mechanics · angular-momentum-squared-identity

Problem

Verify the identity L^2=r^×p^⋅r^×p^=r^2p^2−(r^⋅p^)2+iℏr^⋅p^\hat{L}^2 = \hat{\mathbf{r}} \times \hat{\mathbf{p}} \cdot \hat{\mathbf{r}} \times \hat{\mathbf{p}} = \hat{r}^2 \hat{p}^2 - (\hat{\mathbf{r}} \cdot \hat{\mathbf{p}})^2 + i\hbar \hat{\mathbf{r}} \cdot \hat{\mathbf{p}}

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