Franz Schwabl Quantum Mechanics 4th Edit · Problem 2.8

One-Dimensional Problems

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

Problem

For the operators

p_i = \frac{\hbar}{\mathrm{i}}\partial_i \quad \text{and} \quad L_i = \varepsilon_{ijk}\, x_j p_k\,,

compute the commutators

[p_i^2, f(\boldsymbol{x})] \quad \text{and} \quad [L_i, L_j]\,.