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Prog. Theor. Phys. Vol. 119 No. 4 (2008) pp. 663-700

[ Full Text PDF : FREE ACCESS (427K) ]

Exactly Solvable `Discrete' Quantum Mechanics; Shape Invariance, Heisenberg Solutions, Annihilation-Creation Operators and Coherent States

Satoru Odake1 and Ryu Sasaki2

1Department of Physics, Shinshu University, Matsumoto 390-8621, Japan
2Yukawa Institute for Theoretical Physics, Kyoto University,
Kyoto 606-8502, Japan

(Received February 12, 2008)

Abstract:

Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states. The eigenfunctions are the (q-)Askey-scheme of hypergeometric orthogonal polynomials satisfying difference equation versions of the Schrödinger equation. Various reductions (restrictions) of the symmetry algebra of the Askey-Wilson system are explored in detail.


URL : http://ptp.ipap.jp/link?PTP/119/663/
DOI : 10.1143/PTP.119.663

[ Full Text PDF : FREE ACCESS (427K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 122 No. 5 (2009) pp. 1067-1079 :
    Crum's Theorem for `Discrete' Quantum Mechanics
    Satoru Odake and Ryu Sasaki
  2. Progress of Theoretical Physics Vol. 124 No. 1 (2010) pp. 1-26 :
    Modification of Crum's Theorem for `Discrete' Quantum Mechanics
    Leonor García-Gutiérrez, Satoru Odake and Ryu Sasaki
  3. Progress of Theoretical Physics Vol. 125 No. 5 (2011) pp. 851-870 :
    The Exceptional (Xℓ) (q)-Racah Polynomials
    Satoru Odake and Ryu Sasaki
  4. Progress of Theoretical Physics Vol. 126 No. 1 (2011) pp. 1-34 :
    Dual Christoffel Transformations
    Satoru Odake and Ryu Sasaki

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