Extended trigonometric Cherednik algebras and nonstationary Schroedinger equations with delta-potentials
- Department of Mathematics, University of California, Riverside, CA 92521 (United States)
- Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands and IMAPP, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands)
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 Schroedinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schroedinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations as functions of the momenta. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with delta-function interactions is indicated.
- OSTI ID:
- 22162760
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 2; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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