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

U. Carow-Watamura; M. Schlieker; S. Watamura

doi:10.1007/BF01549697

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

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

Research output: Contribution to journal › Article › peer-review

84 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	439-446
Number of pages	8
Journal	Zeitschrift für Physik C Particles and Fields
Volume	49
Issue number	3
DOIs	https://doi.org/10.1007/BF01549697
Publication status	Published - 1991 Sep 1
Externally published	Yes

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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10.1007/BF01549697

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title = "SOq(N) covariant differential calculus on quantum space and quantum deformation of schr{\"o}dinger equation",

abstract = "We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SOq(N) is acting. The differential calculus is required to be manifestly covariant under SOq(N) transformations. Using this calculus, we consider the Schr{\"o}dinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions.",

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year = "1991",

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N2 - We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SOq(N) is acting. The differential calculus is required to be manifestly covariant under SOq(N) transformations. Using this calculus, we consider the Schrödinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions.

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

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

Abstract

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