JEDNOSTKA NAUKOWA KATEGORII A+

Spectrum generating functions for oscillators in Wigner's quantization

Tom 93 / 2011

Stijn Lievens, Joris Van der Jeugt Banach Center Publications 93 (2011), 189-197 MSC: Primary 81R05; Secondary 81R15. DOI: 10.4064/bc93-0-15

Streszczenie

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 $\def\osp{\mathfrak{osp}}\osp(1|2n)$ generators, and also recall the solution in terms of $\def\gl{\mathfrak{gl}}\gl(1|n)$ 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.

Autorzy

  • Stijn LievensInstitute of Mathematics, Statistics and Actuarial Science
    University of Kent
    Cornwallis Building
    Kent CT2 7NF, United Kingdom
    e-mail
  • Joris Van der JeugtDepartment of Applied Mathematics and Computer Science
    Ghent University
    Krijgslaan 281-S9
    B-9000 Gent, Belgium
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek