Advanced Quantum Mechanics Schwabl · Problem 7.1

The Coulomb Potential

Physics — Quantum Mechanics · angular-momentum-dirac-hamiltonian

Problem

Show, by explicit calculation of the commutator, that the total angular momentum

\mathbf{J} = \mathbf{x} \times \mathbf{p}\,\mathbb{1} + \frac{\hbar}{2}\boldsymbol{\Sigma}

commutes with the Dirac Hamiltonian for a central potential

H = c\left(\sum_{k=1}^{3} \alpha^k p^k + \beta mc\right) + e\Phi(|\mathbf{x}|)\,.