Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials

Details Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials

2011-04-28

arxiv.org/abs/1104.5489v1

Mathematics

Representation Theory

23 pages

Scientific paper

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 Schr\"odinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schr\"odinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations in their spectral parameter. The relation to the vector valued root system analogs of the Lieb-Liniger model on the circle is indicated.

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