Crum's Theorem for `Discrete' Quantum Mechanics
arXiv:0902.2593 · doi:10.1143/PTP.122.1067
Abstract
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 Schrödinger equation is a difference equation.
13 pages, to be published in Prog.Theor.Phys., several comments and references added