Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with deltapotentials
Abstract
We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schrödinger equation with deltapotential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schrödinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference KnizhnikZamolodchikov equations as functions of the momenta. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with deltafunction interactions is indicated.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 February 2013
 DOI:
 10.1063/1.4790566
 arXiv:
 arXiv:1104.5489
 Bibcode:
 2013JMP....54b1702H
 Keywords:

 algebra;
 boson systems;
 mathematical operators;
 Schrodinger equation;
 05.30.Jp;
 02.20.Uw;
 03.65.Fd;
 03.65.Ge;
 Boson systems;
 Quantum groups;
 Algebraic methods;
 Solutions of wave equations: bound states;
 Mathematics  Representation Theory;
 Mathematical Physics
 EPrint:
 23 pages