1999/09/07 by C. Quesne · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Limiting #Linear algebra #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Normalization (sociology) #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #hep-th #math-ph #math.MP #math.QA #quant-ph
paper · pdf · doi:10.1088/0305-4470/32/38/401
published as J. Phys. A 32 (1999) 6705-6710 · 9 pages, LaTeX, no figures
openalex publication_date 1999/09/07 · arxiv created 1999/11/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We comment on a recent paper by Chen et al (1998 J. Phys. A: Math. Gen. 31 6473), wherein a nonlinear deformation of su (1,1) involving two deforming functions is realized in the exactly solvable quantum-mechanical problem with Pöschl-Teller potential, and is used to derive the well known su (1,1) spectrum-generating algebra of this problem. We show that one of the defining relations of the nonlinear algebra, presented by the authors, is only valid in the limiting case of an infinite square well, and we determine the correct relation in the general case. We also use it to establish the correct link with su (1,1), as well as to provide an algebraic derivation of the eigenfunction normalization constant.