TY - GEN UR - http://lib.ugent.be/catalog/pug01:3213271 ID - pug01:3213271 LA - eng TI - Spectrum generating functions for oscillators in Wigner's quantization PY - 2011 SN - 9788386806126 PB - Warsaw AU - Lievens, Stijn AU - Van der Jeugt, Joris WE02 801000490010 0000-0003-1387-1676 AU - Abramov, Viktor editor AU - Fuchs, Jurgen editor AU - Paal, Eugen editor AU - Stolin, Alexander editor AU - Tralle, Aleksy editor AB - The n-dimensional (isotropic and non-isotropic) harmonic oscillator is studied as a Wigner quantum system. In particular, we focus on the energy spectrum of such systems. We show how to solve the compatibility conditions in terms of osp(1|2n) generators, and also recall the solution in terms of gl(1|n) generators. A method is described for determining a spectrum generating function for an element of the Cartan subalgebra when working with a representation of any Lie (super)algebra. Here, the character of the representation at hand plays a crucial role. This method is then applied to the n-dimensional isotropic harmonic oscillator, yielding explicit formulas for the energy eigenvalues and their multiplicities. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 3213271 | ||
005 | 20170102095237.0 | ||
008 | 130515s2011------------------------eng-- | ||
020 | a 9788386806126 | ||
024 | a 1854/LU-3213271 2 handle | ||
024 | a 10.4064/bc93-0-15 2 doi | ||
040 | a UGent | ||
245 | a Spectrum generating functions for oscillators in Wigner's quantization | ||
260 | a Warsaw, Poland b Polish Academy of Sciences. Institute of Mathematics c 2011 | ||
520 | a The n-dimensional (isotropic and non-isotropic) harmonic oscillator is studied as a Wigner quantum system. In particular, we focus on the energy spectrum of such systems. We show how to solve the compatibility conditions in terms of osp(1|2n) generators, and also recall the solution in terms of gl(1|n) generators. A method is described for determining a spectrum generating function for an element of the Cartan subalgebra when working with a representation of any Lie (super)algebra. Here, the character of the representation at hand plays a crucial role. This method is then applied to the n-dimensional isotropic harmonic oscillator, yielding explicit formulas for the energy eigenvalues and their multiplicities. | ||
598 | a C1 | ||
100 | a Lievens, Stijn | ||
700 | a Van der Jeugt, Joris u WE02 0 801000490010 0 0000-0003-1387-1676 | ||
700 | a Abramov, Viktor e editor | ||
700 | a Fuchs, Jurgen e editor | ||
700 | a Paal, Eugen e editor | ||
700 | a Stolin, Alexander e editor | ||
700 | a Tralle, Aleksy e editor | ||
650 | a Mathematics and Statistics | ||
653 | a spectrum generating functions | ||
653 | a Wigner quantum oscillator | ||
653 | a osp(1|2n) | ||
773 | t Baltic-Nordic workshop on Algebra, Geometry and Mathematical Physics g Banach Center Publications. 2011. Polish Academy of Sciences. Institute of Mathematics. 93 p.189-197 q 93:<189 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/3213271/file/3213282 z [ugent] y lievens-vdjeugt.pdf | ||
920 | a confcontrib | ||
852 | x WE b WE02 | ||
922 | a UGENT-WE |
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