相关论文: Integral formulas for wave functions of quantum ma…
In this paper the quantum integrals of the Hamiltonian of the quantum many-body problem with the interaction potential K/sinh^2(x) (Sutherland operator) are constructed as images of higher Casimirs of the Lie algebra gl(N) under a certain…
We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland…
The Hamiltonian of the quantum Calogero-Sutherland model of $N$ identical particles on the circle with $1/r^{2}$ interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials…
We derive explicit formulas for the eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland model as infinite series, to all orders and for arbitrary particle numbers and coupling parameters. The eigenfunctions obtained provide…
The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the…
We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the…
Various infinite-dimensional versions of the Calogero-Moser operator are discussed. The related class of Jack-Laurent symmetric functions is studied. In the special case when parameter k=-1 the analogue of Jacobi-Trudy formula is given and…
We construct a linear basis for the polynomial eigenfunctions of a family of deformed Calogero-Moser-Sutherland operators naturally associated with hypergeometric polynomials. In our construction the eigenfunctions are obtained as linear…
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms…
The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m),…
We consider the Jack--Laurent symmetric functions for special values of parameters p_0=n+k^{-1}m, where k is not rational and m and n are natural numbers. In general, the coefficients of such functions may have poles at these values of p_0.…
Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions…
We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling…
We use generalized kernel functions to construct explicit solutions by integrals of the non-stationary Schr\"odinger equation for the Hamiltonian of the elliptic Calogero-Sutherland model (also known as elliptic…
There exists a large class of quantum many-body systems of Calogero-Sutherland type where all particles can have different masses and coupling constants and which nevertheless are such that one can construct a complete (in a certain sense)…
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra $D_4$ in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra.…
A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric…
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier…
We obtain certain Mellin-Barnes integrals which present wave functions for $GL(n,\mathbb{R})$ hyperbolic Sutherland model with arbitrary positive coupling constant.
Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the $BC_n$ root system), we arrive -- via partial confluent limits in the sense of Oshima and Shimeno -- at solutions of the…