14 citations · 55 across the 9 of their papers we have counts for
9 papers
Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
Farrokh Atai, Martin Hallnäs, Edwin Langmann
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctio…
Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation
Farrokh Atai, Edwin Langmann
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…
Source identities and kernel functions for the deformed Koornwinder-van Diejen models
F. Atai
We consider generalizations of the -type relativistic Calogero-Moser-Sutherland models, comprising of the rational, trigonometric, hyperbolic, and elliptic cases, due to Koornw…
Orthogonality of super-Jack polynomials and a Hilbert space interpretation of deformed Calogero-Moser-Sutherland operators
Farrokh Atai, Martin Hallnäs, Edwin Langmann
We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials with respect to a natural positive semi-d…
Integral representation of solution to the non-stationary Lamé equation
Farrokh Atai
We consider methods for constructing explicit solutions of the non-stationary Lamé equation, which is a generalization of the classical Lamé equation, that has appeared in works on…
Series Solutions of the Non-Stationary Heun Equation
Farrokh Atai, Edwin Langmann
We consider the non-stationary Heun equation, also known as quantum Painlevé VI, which has appeared in different works on quantum integrable models and conformal field theory. We u…
Deformed Calogero-Sutherland model and fractional Quantum Hall effect
Farrokh Atai, Edwin Langmann
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases.…
Source identities and kernel functions for deformed (quantum) Ruijsenaars models
F. Atai, M. Hallnäs, E. Langmann
We consider the relativistic generalization of the quantum Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic…
Variational orthogonalization
Farrokh Atai, Jens Hoppe, Mariusz Hynek +1
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximate…