Unified theory of annihilation-creation operators for solvable (“discrete”) quantum mechanics

DOI10.1063/1.2349485zbMath1112.81065arXivquant-ph/0605215OpenAlexW2124341353MaRDI QIDQ3442046

Ryu Sasaki, Satoru Odake

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0605215

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (11)

New Quasi-Exactly Solvable Difference Equation ⋮ Discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts ⋮ Recurrence relations of the multi-indexed orthogonal polynomials V: Racah and q -Racah types ⋮ Exact Heisenberg operator solutions for multiparticle quantum mechanics ⋮ Recurrence relations of the multi-indexed orthogonal polynomials. VI. Meixner–Pollaczek and continuous Hahn types ⋮ Discrete orthogonality relations for multi-indexed Laguerre and Jacobi polynomials ⋮ Prepotential approach to exact and quasi-exact solvabilities ⋮ Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials ⋮ Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach ⋮ Exactly and quasi-exactly solvable ‘discrete’ quantum mechanics ⋮ Multi-indexed Meixner and littleq-Jacobi (Laguerre) polynomials

Cites Work

• Quantum Calogero-Moser models: integrability for all root systems
• Calogero-Moser Models. V: Supersymmetry and Quantum Lax Pair
• Equilibrium positions, shape invariance and Askey–Wilson polynomials
• A search for shape-invariant solvable potentials
• Integrability of difference Calogero–Moser systems
• Calogero-Sutherland oscillator: classical behaviour and coherent states
• Generalized coherent and intelligent states for exact solvable quantum systems
• Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials
• Newton-equivalent Hamiltonians for the harmonic oscillator

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