The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group
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| Natura: | Artículo científico |
| Lingua: | en |
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Sociedade Brasileira de Física
2013
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| _version_ | 1876429740967985152 |
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| author | R. G. G. Amorim |
| author_facet | R. G. G. Amorim |
| contents | The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group R. G. G. Amorim S. C. Ulhoa A. E. Santana Física, Astronomía y Matemáticas Phase space Moyal product Quantum fields We study symplectic unitary representations for the Galilei group and derive the Schr¨odinger equation in phase space. Our formalism is based on the noncommutative structure of the star product. Guided by group theoretical concepts, we construct a physically consistent phase-space theory in which each state is described by a quasi-probability amplitude associated with the Wigner function. As applications, we derive the Wigner functions for the 3D harmonic oscillator and the noncommutative oscillator in phase space. 2013 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46425766005 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.1-2 Vol.43 |
| format | Artículo científico |
| id | redalyc_46425766005 |
| institution | Redalyc |
| language | en |
| publishDate | 2013 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group R. G. G. Amorim Física, Astronomía y Matemáticas Phase space Moyal product Quantum fields The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group R. G. G. Amorim S. C. Ulhoa A. E. Santana Física, Astronomía y Matemáticas Phase space Moyal product Quantum fields We study symplectic unitary representations for the Galilei group and derive the Schr¨odinger equation in phase space. Our formalism is based on the noncommutative structure of the star product. Guided by group theoretical concepts, we construct a physically consistent phase-space theory in which each state is described by a quasi-probability amplitude associated with the Wigner function. As applications, we derive the Wigner functions for the 3D harmonic oscillator and the noncommutative oscillator in phase space. 2013 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46425766005 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.1-2 Vol.43 |
| title | The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group |
| topic | Física, Astronomía y Matemáticas Phase space Moyal product Quantum fields |
| url | https://www.redalyc.org/articulo.oa?id=46425766005 |