Franz Schwabl Quantum Mechanics 4th Edit · Problem 5.5

The Central Potential I

Physics — Quantum Mechanics · angular-momentum-commutators-vector-operator

Problem

Show the following: (a) For a vector operator

\boldsymbol{V}(\boldsymbol{x},\boldsymbol{p})

[\boldsymbol{L}^2,\boldsymbol{V}] = 2\mathrm{i}\hbar(\boldsymbol{V}\times\boldsymbol{L} - \mathrm{i}\hbar\boldsymbol{V}).

(b)

[L_i, p_j] = \mathrm{i}\hbar\varepsilon_{ijk}p_k