Heun Equation and Inozemtsev Models
نویسنده
چکیده
The BCN elliptic Inozemtsev model is a quantum integrable systems with N -particles whose potential is given by elliptic functions. Eigenstates and eigenvalues of this model are investigated.
منابع مشابه
On the Heun equation.
A new approach to the theory of finite-gap integration for the Heun equation is constructed. As an application, global monodromies of the Heun equation are calculated and expressed as hyperelliptic integrals. The relationship between the Heun equation and the spectral problem for the BC1 Inozemtsev model is also discussed.
متن کاملThe Heun Equation and the Calogero-moser-sutherland System Iii: the Finite-gap Property and the Monodromy
where ℘(x) is the Weierstrass ℘-function with periods (1, τ), ω0 = 0, ω1 = 1 2 , ω2 = − τ+1 2 , ω3 = τ 2 are half-periods, and li (i = 0, 1, 2, 3) are coupling constants. This model is a one-particle version of the BCN Inozemtsev system [6], which is known to be the universal quantum integrable system with BN symmetry [6, 11]. The BCN Calogero-Moser-Sutherland systems are special cases of BCN I...
متن کاملThe Heun Equation and the Calogero-moser-sutherland System Ii: the Perturbation and the Algebraic Solution
We justify the holomorphic perturbation for the 1particle Inozemtsev model from the trigonometric model and show the holomorphy of the eigenvalues and the eigenfuncions which are obtained by the series expansion. We investigate the relationship between the L 2 space and the nite dimensional space of certain elliptic functions, and determine the distribution of the \algebraic" eigenvalues on the...
متن کاملThe Heun Equation and the Calogero-moser-sutherland System Ii: Perturbation and Algebraic Solution
We apply a method of perturbation for the BC1 Inozemtsev model from the trigonometric model and show the holomorphy of perturbation. Consequently, the convergence of eigenvalues and eigenfuncions which are expressed as formal power series is proved. We investigate also the relationship between L space and some finite dimensional space of elliptic functions.
متن کاملTowards Finite-Gap Integration of the Inozemtsev Model
The Inozemtsev model is considered to be a multivaluable generalization of Heun’s equation. We review results on Heun’s equation, the elliptic Calogero–Moser–Sutherland model and the Inozemtsev model, and discuss some approaches to the finite-gap integration for multivariable models.
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تاریخ انتشار 2008