2019/11/30 by J. -P. Gazeau, T. Koide · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.stat-mech #gr-qc #hep-th
paper · pdf · doi:10.1016/j.aop.2020.168159
published as Ann. Phys. 416, 168159 (2020) · 7 pages, no figure, discussions and references are added
arxiv created 2020/03/16 · arxiv updated 2020/04/09
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 ℏ/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.