Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-09-08
Prog.Theor.Phys.Suppl.118:375-389,1995
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, TU-466
Scientific paper
10.1143/PTPS.118.375
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 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 Schr\"odinger equation and eigenvalues. We also present an alternative way to solve the Schr\"odinger equation which is based on the $q$-analysis. We represent the Schr\"odinger 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.
Carow-Watamura Ursula
Watamura Satoshi
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