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Prog. Theor. Phys. Vol. 124 No. 1 (2010) pp. 1-26

[ Full Text PDF : FREE ACCESS (298K) ]

Modification of Crum's Theorem for `Discrete' Quantum Mechanics

Leonor García-Gutiérrez,1 Satoru Odake2 and Ryu Sasaki1

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

(Received April 5, 2010; Revised June 3, 2010)

Abstract:

Crum's theorem in one-dimensional quantum mechanics asserts the existence of an associated Hamiltonian system for any given Hamiltonian with the complete set of eigenvalues and eigenfunctions. The associated system is iso-spectral to the original one except for the lowest energy state, which is deleted. A modification due to Krein-Adler provides algebraic construction of a new complete Hamiltonian system by deleting a finite number of energy levels. Here we present a discrete version of the modification based on Crum's theorem for the `discrete' quantum mechanics developed by two of the present authors.

Subject Index : 010, 012, 064
URL : http://ptp.ipap.jp/link?PTP/124/1/
DOI : 10.1143/PTP.124.1

[ Full Text PDF : FREE ACCESS (298K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 125 No. 5 (2011) pp. 851-870 :
    The Exceptional (Xℓ) (q)-Racah Polynomials
    Satoru Odake and Ryu Sasaki
  2. Progress of Theoretical Physics Vol. 126 No. 1 (2011) pp. 1-34 :
    Dual Christoffel Transformations
    Satoru Odake and Ryu Sasaki
  3. Progress of Theoretical Physics Vol. 126 No. 2 (2011) pp. 185-201 :
    Prepotential Approach to Solvable Rational Potentials and Exceptional Orthogonal Polynomials
    Choon-Lin Ho

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