8 papers
Quasi-Exactly Solvable Models with Spin-Orbital Interaction
Alexander Ushveridze
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discuss…
Bethe Ansatz in Quantum Mechanics. 2. Construction of Multi-Parameter Spectral Equations
Dieter Mayer, Alexander Ushveridze, Zbigniew Walczak
In this paper we propose a simple method for building exactly solvable multi-parameter spectral equations which in turn can be used for constructing completely integrable and exact…
Bethe Ansatz in Quantum Mechanics. 1. The Inverse Method of Separation of Variables
Dieter Mayer, Alexander Ushveridze
In this paper we formulate a general method for building completely integrable quantum systems. The method is based on the use of the so-called multi-parameter spectral equations,…
Infinite Quasi-Exactly Solvable Models
H. D. Doebner, K. Lazarow, A. G. Ushveridze
We introduce a new concept of infinite quasi-exactly solvable models which are constructable through multi-parameter deformations of known exactly solvable ones. The spectral probl…
Statistical Topology of Real Polynomials. I: Two Variables
George Khimshiashvili, Alexander Ushveridze
We investigate average gradient degree of normal random polynomials of fixed algebraic degree n. In particular, for polynomials of two variables, asymptotics of the average gradien…
Bender-Dunne Orthogonal Polynomials and Quasi-Exact Solvability
A. Krajewska, A. Ushveridze, Z. Walczak
The paper is devoted to the further study of the remarkable classes of orthogonal polynomials recently discovered by Bender and Dunne. We show that these polynomials can be generat…