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1997 | 40 | 1 | 403-413
Tytuł artykułu

Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.
Słowa kluczowe
Rocznik
Tom
40
Numer
1
Strony
403-413
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Sektion Physik, Universität München, LS Prof. Wess, Theresienstr. 37, D-80333 München, Germany
Bibliografia
  • [1] J. Schwenk, J. Wess, A Quantum Mechanical toy model, Phys. Lett., B 291 (1992) 273.
  • [2] A. Hebecker, S. Schreckenberg, J. Schwenk, W. Weich, J. Wess, Representations of a q-deformed Heisenberg Algebra, MPI-Ph/93-45, (1993).
  • [3] M. Fichtmueller, A. Lorek and J. Wess, Q-deformed Phase Space and its Lattice Structure, MPI-PhT/95-109.
  • [4] Tom H. Koornwinder, Orthogonal Polynomials in Connection with Quantum Groups, P. Nevai (ed.), Orthogonal Polynomials,Kluwer Academic Publishers, (1990) 257-292.
  • [5] Roelof Koekoek and René F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Delft University of Technology, Reports of the faculty of technical Mathematics and Informatics no 94-05, (1994).
  • [6] Gasper and Rahman, Basic Hypergeometric Series, Cambridge University Press, (1990).
  • [7] A. Macfarlane, On q-analogues of the quantum harmonic oscillator and the quantum group $SU_q(2)$, J. Phys., A 22 (1989) 4581.
  • [8] P. P. Kulish, On Recent Progress in Quantum Groups an introductory review, Jahrbuch Überblicke Mathematik 1993, Vieweg, (1993) 97.
  • [9] T. Curtwright, C. Zachos, Paradigms of Quantum Algebras, ANL-HEP-PR-90-61, (1990).
  • [10] Gaetano Fiore, The $SO_q(N, ℝ)$-Symmetric Harmonic Oscillator on the Quantum Euclidean Space $ℝ^N_q$ and It's Hilbert Space Structure, International Journal of Modern Physics, Vol. 8, 26 (1993) 4679-4729.
  • [11] Joachim Seifert, Quantum Mechanical Representations of the Q-Oscillator, forthcoming publication.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv40z1p403bwm
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