Minimum uncertainties states of angular momentum and angular position

Abstract

The states of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position and momentum, that is the intelligent states, are also the states that minimize the uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the minimum uncertainty product states for the angular case by means of instructive approximations, a numerical terative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.