The Quantum Group as a Symmetry | Zendy

Ursula Carow-Watamura | Zendy; Satoshi Watamura | Zendy

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The Quantum Group as a Symmetry

Author(s) -

Ursula Carow-Watamura,

Satoshi Watamura

Publication year - 1995

Publication title -

progress of theoretical physics supplement

Language(s) - English

Resource type - Journals

ISSN - 0375-9687

DOI - 10.1143/ptps.118.375

Subject(s) - eigenfunction , eigenvalues and eigenvectors , harmonic oscillator , schrödinger equation , mathematical physics , mathematics , symmetry group , differential equation , creation and annihilation operators , euclidean space , quantum , quantum harmonic oscillator , partial differential equation , hilbert space , quantum mechanics , mathematical analysis , physics , geometry

With the aim to construct a dynamical model with quantum group symmetry, the$q$-deformed Schr\"odinger equation of the harmonic oscillator on the$N$-dimensional quantum Euclidian space is investigated. After reviewing thedifferential calculus on the $q$-Euclidian space, the $q$-analog of thecreation-annihilation operator is constructed. It is shown that it producessystematically all eigenfunctions of the Schr\"odinger equation andeigenvalues. We also present an alternative way to solve the Schr\"odingerequation which is based on the $q$-analysis. We represent the Schr\"odingerequation by the $q$-difference equation and solve it by using $q$-polynomialsand $q$-exponential functions. The problem of the involution corresponding tothe reality condition is discussed.Comment: LaTeX, TU-46

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