2019/07/31 by Satoru Odake · 7 citations
Mathematics · Physics and Astronomy · #Eigenfunction #Hilbert space #Integer (computer science) #Invariant (physics) #Mathematical functions and polynomials #Orthogonal basis #Orthogonal polynomials #Quantum #Quantum Mechanics and Non-Hermitian Physics #Set (abstract data type) #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.CA #math.MP #nlin.SI
paper · pdf · doi:10.1093/ptep/ptz124
published in Progress of Theoretical and Experimental Physics 2019(12) (University of Oxford) · 27 pages. Comments added, typo corrected. To appear in PTEP
openalex created_date 2019/08/13 · arxiv created 2019/10/11 · openalex publication_date 2019/10/11 · arxiv updated 2020/06/23 · openalex updated_date 2026/08/05
Abstract We present new exactly solvable systems of the discrete quantum mechanics with pure imaginary shifts, whose physical range of coordinates is a whole real line. These systems are shape invariant and their eigenfunctions are described by the multi-indexed continuous Hahn and Meixner–Pollaczek orthogonal polynomials. The set of degrees of these multi-indexed polynomials is \ℓD,ℓD+1,ℓD+2,…\, where ℓD is an even positive integer (D: a multi-index set), but they form a complete set of orthogonal basis in the weighted Hilbert space.