The Quantum Group as a Symmetry : The Schrodinger Equation of the N-Dimensional q-Deformed Harmonic Oscillator

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概要

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• With the aim to construct a dynamical model with quantum group symmetry, the q-deformed Schrodinger equation of the harmonic oscillator on the N-dimensional quantum Euclidian space is investigated. After reviewing the differential calculus on the q-Euclidian space, the q-analog of the creation-annihilation operator is constructed. It is shown that it produces systematically all eigenfunctions of the Schrodinger equation and eigenvalues. We also present an alternative way to solve the Schrodinger equation which is based on the q-analysis. We represent the Schrodinger equation by the q-difference equation and solve it by using q-polynomials and q-exponential functions. The problem of the involution corresponding to the reality condition is discussed.

• 理論物理学刊行会の論文
• 1995-06-26

著者

• Carow-watamura Ursula

  Fakultat Fur Physik University Freiburg

• WATAMURA Satoshi

  Institute of Physics, University of Tokyo

• WATAMURA Satoshi

  Forschungsinstitut fur Mathematik, ETH-Zentrum

• Watamura S

  Forschungsinstitut Fur Mathematik Eth-zentrum : Department Of Physics Tohoku University : The Canon

関連論文

• Gauge Boson Condensation and Symmetry Breaking Patterns in Non-Abelian Gauge Theories
• Hopf Algebra Symmetry and String Theory(General and Mathematical Physics)
• The Quantum Group as a Symmetry : The Schrodinger Equation of the N-Dimensional q-Deformed Harmonic Oscillator

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