Uncertainty relation for angle from a quantum-hydrodynamical perspective
| Autor: | Jean-Pierre Gazeau, Tomoi Koide |
|---|---|
| Přispěvatelé: | AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Observatoire de Paris, PSL Research University (PSL)-PSL Research University (PSL)-Université Paris Diderot - Paris 7 (UPD7) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Angular momentum hydrodynamics: quantum 02.50.Ey General Physics and Astronomy FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) angular momentum 01 natural sciences General Relativity and Quantum Cosmology 11.10.Ef Variational principle 0103 physical sciences stochastic Statistical physics stochastic calculus 010306 general physics uncertainty relations Quantum Eigenvalues and eigenvectors Condensed Matter - Statistical Mechanics Physics variational principle Quantum Physics Statistical Mechanics (cond-mat.stat-mech) 010308 nuclear & particles physics [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Operator (physics) variational [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] Variational method High Energy Physics - Theory (hep-th) 03.65.Ca Quantum hydrodynamics [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc] uncertainty relation Polar coordinate system Quantum Physics (quant-ph) |
| Zdroj: | Annals Phys. Annals Phys., 2020, 416, pp.168159. ⟨10.1016/j.aop.2020.168159⟩ |
| DOI: | 10.1016/j.aop.2020.168159⟩ |
| Popis: | 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. Comment: 7 pages, no figure, discussions and references are added |
| Databáze: | OpenAIRE |
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