On the n-particle Wigner quantum oscillator: non-commutative coordinates and particle localisation
Van der Jeugt, J., King, R.C., Stoilova, N.I. and Palev, T.D. (2004) On the n-particle Wigner quantum oscillator: non-commutative coordinates and particle localisation. In, Doebner, H.-D. and Dobrev, V. (eds.) Lie Theory and its Applications in Physics V: Proceedings of the Fifth International Workshop, Varna, Bulgaria 16-22 June 2003. Lie Theory and its Applications in Physics V, Fifth International Workshop Singapore, World Scientific Publishing, 4337-4362.
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Description/Abstract
After a general introduction to Wigner Quantum Systems, we define the three-dimensional n-particle Wigner Quantum Oscillator, and its relation to the Lie superalgebra sl(1|3n). In this framework, coordinates, momentum and the angular momentum of the particles are defined and investigated. This investigation is done in state spaces, using representation theory of sl(1|3n). For the case of n=1, the main properties are listed, with an emphasis on the non-commutative coordinates of the particle and its unconventional consequences. For general n, we study energy spectra, angular momentum, and in particular the particle configuration and its interpretation. Throughout, a comparison with the canonical oscillator solution is given.
| Item Type: | Book Section |
|---|---|
| Related URLs: | http://www.worldscibooks.com/p.../5603.html |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics |
| ePrint ID: | 29533 |
| Deposited On: | 19 May 2006 |
| Last Modified: | 02 Jul 2010 02:59 |
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