Volume 1, Issue 1, April 2015, Page: 1-8
Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics
Raoelina Andriambololona, Theoretical Physics Dept., Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Ravo Tokiniaina Ranaivoson, Theoretical Physics Dept., Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Rakotoson Hanitriarivo, Theoretical Physics Dept., Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Wilfrid Chrysante Solofoarisina, Theoretical Physics Dept., Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Received: Mar. 10, 2015;       Accepted: Mar. 31, 2015;       Published: Apr. 8, 2015
DOI: 10.11648/j.ijamtp.20150101.11      View  7923      Downloads  238
Abstract
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions. Then we introduce the concept of isodispersion linear canonical transformation.
Keywords
Linear Canonical Transformation, Phase Space Representation, Quantum Mechanics, Operators, States, Wave Functions, Integral Transform, Dispersions
To cite this article
Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Rakotoson Hanitriarivo, Wilfrid Chrysante Solofoarisina, Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics, International Journal of Applied Mathematics and Theoretical Physics. Vol. 1, No. 1, 2015, pp. 1-8. doi: 10.11648/j.ijamtp.20150101.11
Reference
[1]
Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Rakotoson Hanitriarivo, Roland Raboanary,"Study on a Phase Space Representation ofQuantum Theory, "International Journal of Latest Research in Science and TechnologyVolume 2, Issue 2: pp26-35, 2013
[2]
Raoelina Andriambololona “Mécaniquequantique”, Collection LIRA, INSTN Madagascar.pp 25.387-394,1990
[3]
Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Rakotoson Hanitriarivo. “Time-Frequency analysis and harmonic Gaussian functions”,Pure and Applied MathematicsJournal.Vol. 2, No. 2,2013, pp. 71-78. doi: 10.11648/j.pamj.20130202.14
[4]
E.P. Wigner, "On the quantum correction for thermodynamic equilibrium", Phys. Rev 40, 749-759, 1932
[5]
H.J. Groenewold, "On the Principles of elementary quantum mechanics",Physica 12, 1946
[6]
J.E. Moyal, "Quantum mechanics as a statistical theory", Proceedings of the Cambridge Philosophical Society 45, 99–124, 1949
[7]
T.L Curtright ,C.K. Zachos,“ Quantum Mechanics in Phase Space“, arXiv:1104.5269v2 [physics.hist-ph]”, 2011.
[8]
D.Dragoman, “Phase space formulation of quantum mechanics, Insight into the measurement problem”, PhysicaScripta 72, 290–295,2005
[9]
A. Nassimi, “Quantum Mechanics in Phase Space”, arXiv:0706.0237[quant-ph], 2008
[10]
H.-W. Lee, “Theory and application of the quantum phase-space distribution functions”, Phys.Rep 259, Issue 3, 147-211, 1995
[11]
A.Kenfack, K.Zyczkowski, “Negativity of the Wigner function as an indicator of non-classicality”,Journal of Optics B: Quantum Semiclass. Opt. 6, 396–404,2004.
[12]
D. I. Bondar, R.Cabrera, D. V. Zhdanov, H. A. Rabitz, “Wigner function's negativity reinterpreted: Non-conservation as quantumefficiency indicator”, arXiv:1202.3628v3 ,[quant-ph], 2013.
[13]
V. Ashok Narayanan, K.M.M. Prabhu, “The fractional Fourier transform: theory, implementation and error analysis”, Microprocessors and Microsystems 27 (2003) 511–521, Elsevier, 2003.
Browse journals by subject