scholarly journals Solving Integral Representations Problems for the Stationary Schrödinger Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yudong Ren
Keyword(s):  
Schrödinger Equation ◽  
Half Space ◽  
Harmonic Functions ◽  
Schrodinger Equation ◽  
Integral Representations ◽  
Representation Theorems ◽  
Stationary Schrödinger Equation

When solutions of the stationary Schrödinger equation in a half-space belong to the weighted Lebesgue classes, we give integral representations of them, which imply known representation theorems of classical harmonic functions in a half-space.

scholarly journals Exact solutions by integrals of the non-stationary elliptic Calogero–Sutherland equation

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Farrokh Atai ◽  
Edwin Langmann
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Schrodinger Equation ◽  
Kernel Functions ◽  
Integral Representations ◽  
Explicit Solutions ◽  
Jack Polynomials ◽  
Stationary Schrödinger Equation ◽  
Sutherland Model ◽  
Generalized Kernel

Abstract We use generalized kernel functions to construct explicit solutions by integrals of the non-stationary Schrödinger equation for the Hamiltonian of the elliptic Calogero–Sutherland model (also known as elliptic Knizhnik–Zamolodchikov–Bernard equation). Our solutions provide integral representations of elliptic generalizations of the Jack polynomials.

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