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SO q (N) covariant differential calculus on quantum space and quantum deformation of schrödinger equation

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Zeitschrift für Physik C Particles and Fields

Abstract

We construct a differential calculus on theN-dimensional non-commutative Euclidean space, i.e., the space on which the quantum groupSO q (N) is acting. The differential calculus is required to be manifestly covariant underSO q (N) transformations. Using this calculus, we consider the Schrödinger equation corresponding to the harmonic oscillator in the limit ofq→1. The solution of it is given byq-deformed functions.

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Author notes

  1. S. Watamura

    Present address: Department of Physics, College of General Education, Tohoku University, Kawauchi, 980, Sendai, Japan

Authors and Affiliations

  1. Institute for Theoretical Physics, Karlsruhe University, Kaiserstrasse 12, W-7500, Karlsruhe, Federal Republic of Germany

    U. Carow-Watamura, M. Schlieker & S. Watamura

Authors
  1. U. Carow-Watamura
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  2. M. Schlieker
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  3. S. Watamura
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Carow-Watamura, U., Schlieker, M. & Watamura, S. SO q (N) covariant differential calculus on quantum space and quantum deformation of schrödinger equation. Z. Phys. C - Particles and Fields 49, 439–446 (1991). https://doi.org/10.1007/BF01549697

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  • DOI: https://doi.org/10.1007/BF01549697

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