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.
Published in | International Journal of Applied Mathematics and Theoretical Physics (Volume 1, Issue 1) |
DOI | 10.11648/j.ijamtp.20150101.11 |
Page(s) | 1-8 |
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), 2015. Published by Science Publishing Group |
Linear Canonical Transformation, Phase Space Representation, Quantum Mechanics, Operators, States, Wave Functions, Integral Transform, Dispersions
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APA Style
Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Rakotoson Hanitriarivo, Wilfrid Chrysante Solofoarisina. (2015). Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics. International Journal of Applied Mathematics and Theoretical Physics, 1(1), 1-8. https://doi.org/10.11648/j.ijamtp.20150101.11
ACS Style
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. Int. J. Appl. Math. Theor. Phys. 2015, 1(1), 1-8. doi: 10.11648/j.ijamtp.20150101.11
AMA Style
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. Int J Appl Math Theor Phys. 2015;1(1):1-8. doi: 10.11648/j.ijamtp.20150101.11
@article{10.11648/j.ijamtp.20150101.11, author = {Raoelina Andriambololona and Ravo Tokiniaina Ranaivoson and Rakotoson Hanitriarivo and Wilfrid Chrysante Solofoarisina}, title = {Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics}, journal = {International Journal of Applied Mathematics and Theoretical Physics}, volume = {1}, number = {1}, pages = {1-8}, doi = {10.11648/j.ijamtp.20150101.11}, url = {https://doi.org/10.11648/j.ijamtp.20150101.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20150101.11}, 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.}, year = {2015} }
TY - JOUR T1 - Study on Linear Canonical Transformation in a Framework of a Phase Space Representation of Quantum Mechanics AU - Raoelina Andriambololona AU - Ravo Tokiniaina Ranaivoson AU - Rakotoson Hanitriarivo AU - Wilfrid Chrysante Solofoarisina Y1 - 2015/04/08 PY - 2015 N1 - https://doi.org/10.11648/j.ijamtp.20150101.11 DO - 10.11648/j.ijamtp.20150101.11 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 - 1 EP - 8 PB - Science Publishing Group SN - 2575-5927 UR - https://doi.org/10.11648/j.ijamtp.20150101.11 AB - 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. VL - 1 IS - 1 ER -