Franz Schwabl Quantum Mechanics 4th Edit · Problem 5.4

The Central Potential I

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

Problem

Show that the relation

[\boldsymbol{a}\cdot\boldsymbol{L},\, \boldsymbol{b}\cdot\boldsymbol{L}] = \mathrm{i}\hbar(\boldsymbol{a}\times\boldsymbol{b})\cdot\boldsymbol{L}

holds under the assumption that

\boldsymbol{a}

and

\boldsymbol{b}

commute with each other and with

\boldsymbol{L}