Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 2 / 15A / vi

In polar coordinates, $z=r{e}^{i\varphi }$ andConsequentlyThe two states are orthogonal. They are degenerate energy eigenstates, so their coefficients acquire the same overall time-dependent phase; equivalently, $[L,H]=0$ makes $⟨L⟩$ constant. For the normalized statethe angular momentum of a complex-coordinate Gaussian state is therefore