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.

We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schrödinger problems defined by potentials V(x;?,?)=4?2cosh4(x)+V1(?,?)cosh2(x)+???1tanh2(x) and U(x;?,?)=?4?2cos4(x)?V1(?,?)cos2(x)+???1tan2(x), found anti-isospectral transformation of former. use three methods: a direct polynomial expansion, which shows relation between expansion order shape potential function; comparison t...

Heun differential equations are the most general second order Fuchsian with four regular singularities. An explicit integral series representation of functions involving only elementary integrands has hitherto been unknown and noted as an important open problem in a recent review. We provide such representations solutions all class: general, confluent, bi-confluent, doubly triconfluent. All ill...

Abstract This paper is devoted to a complete parametric study of Liouvillian solutions the general trace-free second order differential equation with Laurent polynomial coefficient. family equations, for fixed orders at 0 and $$\infty$$ ∞ polynomial, seen as an affine algebraic variety. We prove that set Pica...

A quantum mechanical model for the Neon-20 nucleus is developed that allows splitting of a bipyramidal structure five alpha-partices into an alpha-particle and Oxygen-16 nucleus. The geometry configuration space assumed to be 3-dimensional spatial wormhole, on wormhole background there attractive short-range potential. This leads radial Schr\"odinger equation Heun form, which simplifies thresho...

In this paper, we determine, at weak coupling, the nonrelativistic $n$-body Schr\"odinger equation that describes low-lying color singlet bound states of two-dimensional adjoint quantum chromodynamics with heavy quarks. case three quarks, show three-body reduces equivalently to a point electric dipole in an field plane angular sector. We conjecture problem is exactly solvable. eigenstates are g...