Quantum theory of rotation angles: The problem of angle sum and angle difference

We reconsider the problem of the sum and difference of two angle variables in quantum mechanics. The spectra of the sum and difference operators have widths of , but angles differing by are indistinguishable. This means that the angle sum and difference probability distributions must be cast into a range. We obtain probability distributions for the angle sum and difference and relate this problem to the representation of nonbijective canonical transformations. Received: 6 December 1997 / Revised: 15 April 1998 / Accepted: 7 May 1998