Crum's Theorem for `Discrete' Quantum Mechanics
Mathematical Physics
2010-02-02 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
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 Schr\"odinger equation is a difference equation.
Cite
@article{arxiv.0902.2593,
title = {Crum's Theorem for `Discrete' Quantum Mechanics},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:0902.2593},
year = {2010}
}
Comments
13 pages, to be published in Prog.Theor.Phys., several comments and references added