Phd Thesis: A kernel function approach to exact solutions of Calogero-Moser-Sutherland type models

by Mr Farrokh Atai (KTH - Theoretical Physics)

Thursday 27 Oct 2016, 10:00 → 14:00 Europe/Stockholm

FR4

This Doctoral thesis gives an introduction to the concept of kernel functions and their significance in the theory of special functions. Of particular interest is the use of kernel function methods for constructing exact solutions of Schrödinger type equations, in one spatial dimension, with interactions governed by elliptic functions. The method is applicable to a large class of exactly solvable systems of Calogero-Moser-Sutherland type, as well as integrable generalizations thereof. It is known that the Schrödinger operators with elliptic potentials have special limiting cases with exact eigenfunctions given by orthogonal polynomials. These special cases are discussed in greater detail in order to explain the kernel function methods with particular focus on the Jacobi polynomials and Jack polynomials.