Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator

Ravo Tokiniaina Ranaivoson; Raoelina Andriambololona; Hanitriarivo Rakotoson

doi:doi:10.11648/j.ijamtp.20180401.12

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Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 1)

Received: 30 November 2017 Accepted: 18 January 2018 Published: 23 February 2018

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Abstract

This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 1)
DOI	10.11648/j.ijamtp.20180401.12
Page(s)	8-14
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Quantum Mechanics, Phase Space Representation, Wavefunction, Eigenvalue Equation, Dispersion Operator

References

[1]	Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Rakotoson Hanitriarivo, Roland Raboanary, "Study on a Phase Space Representation of Quantum Theory", arXiv:1304.1034v3 [quant-ph], International Journal of Latest Research in Science and Technology Volume 2, Issue 2: pp26-35, 2013.
[2]	Hanitriarivo Rakotoson, Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Raboanary Roland, "Coordinate, momentum and dispersion operators in phase space representation", arXiv:1707.02223 [quant-ph], International Journal of Latest Research in Science and Technology ISSN (Online):2278-5299 Volume 6, Issue 4: Page No. 8-13, July-August 2017.
[3]	Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson, Damo Emile Randriamisy, "Dispersion Operator Algebra and Linear Canonical Transformation", arXiv:1608.02268v2 [quant-ph], International Journal of Theoretical Physics, Volume 56, Issue 4, pp 1258–1273, Springer, April 2017.
[4]	RaoelinaAndriambololona, "Mécanique quantique", Collection LIRA, Institut National des Sciences et Techniques Nucléaires (INSTN- Madagascar), 1990.
[5]	E. P. Wigner, "Onthe quantum correction for thermodynamicequilibrium", Phys. Rev 40, 749-759, 1932.
[6]	H. J. Groenewold, "On the Principles of elementary quantummechanics", Physica12, 1946.
[7]	J. E. Moyal, "Quantum mechanics as a statistical theory", Proceedings of the Cambridge Philosophical Society 45, 99–124, 1949.
[8]	G Torres-Vega, J. H. Frederick, "A quantum mechanical representation in phase space", J. Chern. Phys. 98 (4), 1993.
[9]	H.-W. Lee, "Theory and application of the quantum phase-space distribution functions", Phys. Rep 259, Issue 3, 147-211, 1995.
[10]	K. B Moller, T. G Jorgensen, G. Torres-Vega, "On coherent-state representations of quantum mechanics: Wave mechanics in phase space". Journal of Chemical Physics, 106(17), 7228-7240. DOI: 10.1063/1.473684, 1997.
[11]	A. Nassimi, "Quantum Mechanics in Phase Space", arXiv:0706.0237 [quant-ph], 2008.
[12]	T. L Curtright, C. K. Zachos, “Quantum Mechanics in Phase Space”, arXiv:1104.5269v2 [physics. hist-ph]”, 2011.
[13]	D. K. Ferry, “Phase-space functions: can they give a different view of quantum Mechanics”, Journal of Computational Electronics, Volume 14, Issue 4, pp 864 868, December 2015.
[14]	Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Rakotoson Hanitriarivo. "Time- Frequency analysis and harmonic Gaussian functions", Pure and Applied Mathematics Journal. Vol. 2, No. 2, 2013, pp. 71-78. doi: 10.11648/j.pamj.20130202.14.

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Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson. (2018). Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator. International Journal of Applied Mathematics and Theoretical Physics, 4(1), 8-14. https://doi.org/10.11648/j.ijamtp.20180401.12

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ACS Style

Ravo Tokiniaina Ranaivoson; Raoelina Andriambololona; Hanitriarivo Rakotoson. Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator. Int. J. Appl. Math. Theor. Phys. 2018, 4(1), 8-14. doi: 10.11648/j.ijamtp.20180401.12

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AMA Style

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson. Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator. Int J Appl Math Theor Phys. 2018;4(1):8-14. doi: 10.11648/j.ijamtp.20180401.12

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@article{10.11648/j.ijamtp.20180401.12,
  author = {Ravo Tokiniaina Ranaivoson and Raoelina Andriambololona and Hanitriarivo Rakotoson},
  title = {Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {1},
  pages = {8-14},
  doi = {10.11648/j.ijamtp.20180401.12},
  url = {https://doi.org/10.11648/j.ijamtp.20180401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180401.12},
  abstract = {This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.},
 year = {2018}
}

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TY  - JOUR
T1  - Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator
AU  - Ravo Tokiniaina Ranaivoson
AU  - Raoelina Andriambololona
AU  - Hanitriarivo Rakotoson
Y1  - 2018/02/23
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180401.12
DO  - 10.11648/j.ijamtp.20180401.12
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 8
EP  - 14
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180401.12
AB  - This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.
VL  - 4
IS  - 1
ER  -

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Author Information

Ravo Tokiniaina Ranaivoson

Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires, Antananarivo, Madagascar
Raoelina Andriambololona

Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires, Antananarivo, Madagascar
Hanitriarivo Rakotoson

Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires, Antananarivo, Madagascar

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APA Style

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson. (2018). Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator. International Journal of Applied Mathematics and Theoretical Physics, 4(1), 8-14. https://doi.org/10.11648/j.ijamtp.20180401.12

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ACS Style

Ravo Tokiniaina Ranaivoson; Raoelina Andriambololona; Hanitriarivo Rakotoson. Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator. Int. J. Appl. Math. Theor. Phys. 2018, 4(1), 8-14. doi: 10.11648/j.ijamtp.20180401.12

Copy | Download

AMA Style

Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Hanitriarivo Rakotoson. Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator. Int J Appl Math Theor Phys. 2018;4(1):8-14. doi: 10.11648/j.ijamtp.20180401.12

Copy | Download

@article{10.11648/j.ijamtp.20180401.12,
  author = {Ravo Tokiniaina Ranaivoson and Raoelina Andriambololona and Hanitriarivo Rakotoson},
  title = {Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {1},
  pages = {8-14},
  doi = {10.11648/j.ijamtp.20180401.12},
  url = {https://doi.org/10.11648/j.ijamtp.20180401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180401.12},
  abstract = {This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator
AU  - Ravo Tokiniaina Ranaivoson
AU  - Raoelina Andriambololona
AU  - Hanitriarivo Rakotoson
Y1  - 2018/02/23
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180401.12
DO  - 10.11648/j.ijamtp.20180401.12
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 8
EP  - 14
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180401.12
AB  - This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.
VL  - 4
IS  - 1
ER  -

Copy | Download