Related papers: Resonances in the Two-Centers Coulomb Systems
A general new technique to solve the two-center problem with arbitrarily-orientated deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle…
Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…
We study resonant tunneling through quantum-dot systems in the presence of strong Coulomb repulsion and coupling to the metallic leads. Motivated by recent experiments we concentrate on (i) a single dot with two energy levels and (ii) a…
A quantum superintegrable model with reflections on the 2-sphere is introduced. Its two algebraically independent constants of motion generate a central extension of the Bannai--Ito algebra. The Schrodinger equation separates in spherical…
We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…
Quantum--mechanical multiple--well oscillators exhibit curious complex eigenvalues that resemble resonances in models with continuum spectra. We discuss a method for the accurate calculation of their real and imaginary parts.
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…
We develop the complex scaling method for the Dirichlet Laplacian in a domain with asymptotically cylindrical end. We define resonances as discrete eigenvalues of non-selfadjoint operators, obtained as deformations of the selfadjoint…
The purpose of this paper is to prove some results about quantum mechanical black box scattering in even dimensions $d \geq 2$. We study the scattering matrix and prove some identities which hold for its meromorphic continuation onto…
We study the distribution of the eigenvalues inside of the essential spectrum for discrete one-dimensional Schr\"odinger operators with potentials of Coulomb type decay.
It is well known that the resolvent of the free Schr\"odinger operator on weighted $L^2$ spaces has norm decaying like $\lambda^{-\frac{1}{2}}$ at energy $\lambda$. There are several works proving analogous high-frequency estimates for…
One- and two-dimensional operators which originate from the asymptotic form of the three-body Coulomb wave equation in parabolic coordinates are treated within the context of square integrable basis set. The matrix representations of…
In the present article, we consider the so-called two-spin equation that describes four-level quantum systems. Recently, these systems attract attention due to their relation to the problem of quantum computation. We study general…
We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal…
In this note, we compute the Hadamard coefficients of (algebraically) integrable Schrodinger operators in two dimensions. These operators first appeared in [BL] and [B] in connection with Huygens' principle, and our result completes, in a…
We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a…
We calculate accurate eigenvalues and eigenfunctions of the Schr\"odinger equation for a two-dimensional quantum dipole. This model proved useful for the study of elastic effects of a single edge dislocation. We show that the Rayleigh-Ritz…
We report on the first microscopic study of the properties of two-phonon giant resonances in deformed nuclei. The cross sections of the excitation of the giant dipole and the double giant dipole resonances in relativistic heavy ion…
The use of resonators to modify the behavior of electromagnetic systems demonstrates its potential for application in a wide range of problems. However, existing theoretical studies often resort to the single-mode approximation, rarely…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…