Related papers: Exact solution of $D_N$ type quantum Calogero mode…
An array of N subsequent Laguerre polynomials is interpreted as an eigenvector of a non-Hermitian tridiagonal Hamiltonian $H$ with real spectrum or, better said, of an exactly solvable N-site-lattice cryptohermitian Hamiltonian whose…
A class of quasi two and three dimensional quantum lattice spin models with nearest and next nearest neighbour interactions is proposed. The basic idea of construction is to introduce interactions in an array of XXZ spin chains through…
We study the size effect on the energy levels of the D-dimensional isotropic harmonic oscillator confined within a box of radius $r_c$ with impenetrable walls. Two different approaches are used to obtain the energy eigenvalues and…
The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…
We prove sharp analytic regularity and decay at infinity of solutions of variable coefficients nonlinear harmonic oscillators. Namely, we show holomorphic extension to a sector in the complex domain, with a corresponding Gaussian decay,…
We present a surprising redefinition of matrix fermions which brings the supercharges of the $\cal N$-extended supersymmetric $A_{n-1}$ Calogero model introduced in [1] to the standard form maximally cubic in the fermions. The complexity of…
Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp(1|2) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp(1|2) symmetry on a given space…
Recent results are surveyed regarding the spectrum and eigenfunctions of the inverse square Calogero model with harmonic confinement and its relativistic analogue.
We develop an approximate quasi-static theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem…
We discuss several applications and extensions of our previous operator solution of the $N$-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i -…
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
We find a set of the exact eigenfunctions which provide the energy spectrum for the quantum $N$-body Calogero-Sutherland model for fermions or bosons with SU($\nu$) spin degrees of freedom moving in a harmonic confinement potential. The…
New superconformal extensions of d=1 Calogero-type systems are obtained by gauging the U(n) isometry of matrix superfield models. We consider the cases of N=1, N=2 and N=4 one-dimensional supersymmetries. The bosonic core of the N=1 and N=2…
The Hi-Jack symmetric polynomials, which are associated with the simultaneous eigenstates for the first and second conserved operators of the quantum Calogero model, are studied. Using the algebraic properties of the Dunkl operators for the…
In this work we study the homogenization problem for nonlinear eigenvalues of quasilinear elliptic operators. We obtain an explicit order of convergence in $k$ and in $\varepsilon$ for the (variational) eigenvalues.
We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between…
We study the properties of the symplectic sp(2N) algebra deformed using Dunkl operators, which describe the dynamical symmetry of the generalized N-particle quantum Calogero model. It contains a symmetry subalgebra formed by the deformed…
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive…
Recently, Gomez-Ullate et al. (1) have studied a particular N-particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space…
Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the…