The Eigenfunctions of the q-Harmonic Oscillator on the Quantum Line

2004/10/18 by Harald Grosse, Grosse, Harald, Stefan Schraml +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical functions and polynomials #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #hep-th #math.QA #math.SP

paper · pdf · doi:10.48550/arxiv.math/0410389

9 pages, latex

arxiv created 2004/10/18 · openalex publication_date 2004/10/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a complete set of eigenfunctions of the q-deformed harmonic oscillator on the quantum line. In particular the eigenfunctions corresponding to the non-Fock part of the spectrum will be constructed.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

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