Discrete quantum mechanics

A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solutio...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 44; no. 35; pp. 353001 - 47
Main Authors Odake, Satoru, Sasaki, Ryu
Format Journal Article
LanguageEnglish
Published Bristol IOP 02.09.2011
Subjects
Algebra
Exact sciences and technology
Mathematical analysis
Physics
Pictures
Polynomials
Quantum mechanics
Schroedinger equation
Solution space
Symmetry
Hamiltonians
Quantum mechanics
Dynamical symmetry
Unified theory
Annihilation operators
Schroedinger equation
Creation operators
Invariance
Heisenberg picture
Solvability
Orthogonal polynomial
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Summary:A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solution spaces of the Schrodinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schrodinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, and the infinite families of new orthogonal (the exceptional) polynomials. Two newinfinite families of orthogonal polynomials, the X sub(l)Meixner-Pollaczek and the X sub(l)Meixner polynomials, are reported.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/44/35/353001