Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum

Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum

In this work we apply the Dirac method in order to obtain the classical relations for a particle on an ellipsoid. We also determine the quantum mechanical form of these relations by using Dirac quantization. Then by considering the canonical commutation relations between the position and momentum op...

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Bibliographic Details
Published in:Annals of physics Vol. 372; pp. 57 - 67
Main Authors: Panahi, H., Jahangiri, L.
Format: Journal Article
Language:English
Published: New York Elsevier Inc 01-09-2016
Elsevier BV
Subjects:
Bein formalism
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMMUTATION RELATIONS
COMMUTATORS
Dirac method
Ellipsoid
EUCLIDEAN SPACE
Geometric momentum
GEOMETRY
Particle physics
QUANTIZATION
QUANTUM MECHANICS
Quantum physics
Bein formalism
Dirac method
Ellipsoid
Quantum mechanics
Geometric momentum
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Summary:In this work we apply the Dirac method in order to obtain the classical relations for a particle on an ellipsoid. We also determine the quantum mechanical form of these relations by using Dirac quantization. Then by considering the canonical commutation relations between the position and momentum operators in terms of curved coordinates, we try to propose the suitable representations for momentum operator that satisfy the obtained commutators between position and momentum in Euclidean space. We see that our representations for momentum operators are the same as geometric one.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2016.04.013