This should follow from the Lie algebra / Lie group properties of quantum systems, since Angular Momentum is the generator of rotations. I need to clarify this statement.

Proof

  • Write out this proof

Sketch:

  1. Map the impact of Potential invariance to the Hamiltonian
  2. Use the Liouvilleā€“von Neumann equation to calculate .
  3. Use the above to show that angular momentum is constant, i.e.