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

## Abstract

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.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617370

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUTATION RELATIONS; COMMUTATORS; EUCLIDEAN SPACE; GEOMETRY; QUANTIZATION; QUANTUM MECHANICS

### Citation Formats

```
Panahi, H., E-mail: t-panahi@guilan.ac.ir, and Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com.
```*Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum*. United States: N. p., 2016.
Web. doi:10.1016/J.AOP.2016.04.013.

```
Panahi, H., E-mail: t-panahi@guilan.ac.ir, & Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com.
```*Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum*. United States. doi:10.1016/J.AOP.2016.04.013.

```
Panahi, H., E-mail: t-panahi@guilan.ac.ir, and Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com. Thu .
"Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum". United States.
doi:10.1016/J.AOP.2016.04.013.
```

```
@article{osti_22617370,
```

title = {Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum},

author = {Panahi, H., E-mail: t-panahi@guilan.ac.ir and Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com},

abstractNote = {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.},

doi = {10.1016/J.AOP.2016.04.013},

journal = {Annals of Physics},

number = ,

volume = 372,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}

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