Uncertainty relation for angle from a quantum-hydrodynamical perspective

摘要

We revisit the problem of the uncertainty relation for angle by using quantum hydrodynamics formulated in terms of the stochastic variational method (SVM), where we need not define the angle operator. We derive both the Kennard and Robertson-Schrodinger inequalities for canonical variables in polar coordinates. The inequalities have state-dependent minimum values which can be smaller than (sic)/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 coordinates. (C) 2020 Elsevier Inc. All rights reserved.