Source identity and kernel functions for Inozemtsev-type systems
Edwin Langmann, Kouichi Takemura
TL;DR
This paper introduces kernel functions for Inozemtsev Hamiltonians, providing solutions to heat-type equations and deriving exact eigenfunctions and eigenvalues for these elliptic quantum systems.
Contribution
It presents the first kernel functions for Inozemtsev Hamiltonians and solves a heat-type equation that underpins these functions, advancing understanding of elliptic quantum integrable systems.
Findings
Derived kernel functions for Inozemtsev Hamiltonians
Solved a heat-type equation related to these Hamiltonians
Obtained exact eigenfunctions and eigenvalues
Abstract
The Inozemtsev Hamiltonian is an elliptic generalization of the differential operator defining the BC_N trigonometric quantum Calogero-Sutherland model, and its eigenvalue equation is a natural many-variable generalization of the Heun differential equation. We present kernel functions for Inozemtsev Hamiltonians and Chalykh-Feigin-Veselov-Sergeev-type deformations thereof. Our main result is a solution of a heat-type equation for a generalized Inozemtsev Hamiltonian which is the source for all these kernel functions. Applications are given, including a derivation of simple exact eigenfunctions and eigenvalues for the Inozemtsev Hamiltonian.
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