Angular momentum of a complex-coordinate Gaussian state
= Angular momentum of a complex-coordinate Gaussian state
If $\psi=z e^{-r^2/(2a^2)}$ in two dimensions, then $L_z\psi=\hbar\psi$ and $L_z\psi^*=-\hbar\psi^*$. Orthogonality therefore makes the angular-momentum expectation of $\alpha\psi+\beta\psi^*$ equal to $(|\alpha|^2-|\beta|^2)\hbar$ for normalized coefficients.