广义三角Cherednik代数与带δ势的非定常薛定谔方程
Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials
摘要：
我们实现了一个扩展版本的三角Cherednik代数作为仿射Dunkl算子涉及赫维赛德函数。利用扩展的三角Cherednik代数的二次Casimir元定义了一个显式的带δ势的非定常薛定谔方程.利用坐标Bethe方法构造了非定常薛定谔方程的广义Bethe波函数解。证明了广义Bethe波函数的谱参数满足仿射差分Knizhnik-Zamolodchikov方程。指出了量子玻色气体在具有两两δ函数相互作用的圆上的向量值根系类似物的关系。
英文摘要：
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 delta-potential. 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 Knizhnik-Zamolodchikov equations in their spectral parameter. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with pairwise delta-function interactions is indicated.
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