Jean-Pierre Gazeau, Tomoi Koide

Annals of Physics Volume 416, May 2020, 168159

04/04/2020

Abstract

We revisit the problem of the uncertainty relation for angle by using quantum hydrodynamics formulated in the stochastic variational method (SVM), where we need not define the angle operator. We derive both the Kennard and Robertson-Schroedinger inequalities for canonical variables in polar coordinates. The inequalities have state-dependent minimum values which can be smaller than \hbar/2 and then permit a finite uncertainty of angle for the eigenstate of the angular momentum. The present approach provides a useful methodology to study quantum behaviors in arbitrary canonical coordinates.

10.1016/j.aop.2020.168159