Crum's Theorem for `Discrete' Quantum Mechanics

Details Crum's Theorem for `Discrete' Quantum Mechanics Crum's Theorem for `Discrete' Quantum Mechanics

2009-02-16

arxiv.org/abs/0902.2593v2

Prog.Theor.Phys.122:1067-1079,2010

Physics

Mathematical Physics

13 pages, to be published in Prog.Theor.Phys., several comments and references added

Scientific paper

10.1143/PTP.122.1067

In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\"odinger equation is a difference equation.

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