Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
Mathematical Physics
2016-01-22 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions, which are a natural extension of the Euler gamma functions and the q-gamma functions (q-shifted factorials). The dimensions of the orthogonal spaces are finite. These q-orthogonal polynomials are expressed in terms of the Askey-Wilson polynomials and their certain limit forms.
Keywords
Cite
@article{arxiv.1406.2768,
title = {Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1406.2768},
year = {2016}
}
Comments
37 pages. Comments and references added. To appear in J.Math.Phys