Related papers: Resonances in the Two-Centers Coulomb Systems
We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems…
We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint…
The present paper is devoted to the study of resonances for one-dimensional quantum systems with a potential that is the restriction to some large box of an ergodic potential. For discrete models both on a half-line and on the whole line,…
We propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schr\"odinger equations decouple in parabolic and elliptic…
Motivated by recent experiments, in which the Kondo effect has been observed for the first time in a double quantum-dot structure, we study electron transport through a system consisting of two ultrasmall, capacitively-coupled dots with…
We calculate accurate bound states and resonances of two interesting perturbed Coulomb models by means of the Riccati-Pad\'{e} method. This approach is based on a rational approximation to a modified logarithmic derivative of the…
A simple heuristic argument to understand the existence of complex branch points in the $\pi N$ scattering amplitude is presented. It is based on a hypothesis that the singularity structure of the $\pi N$ scattering amplitude is a smooth…
We discuss resonances for Schr\"odinger operators with compactly supported potentials on the line and the half-line. We estimate the sum of the negative power of all resonances and eigenvalues in terms of the norm of the potential and the…
We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using…
Two integrable cases of two-dimensional Schr\"odinger equation with a magnetic field are proposed. Using the polar coordinates and the symmetrical gauge, we will obtain solutions of these equation through Biconfluent and Confluent Heun…
We examine connections between rationality of certain indefinite integrals and equilibrium of Coulomb charges in the complex plane.
We give estimates for the changes of the eigenvalues of the Klein Gordon operator under the change of the potential. In some relevant situations we improve the existing estimates. We test our results on some exactly solvable models (Coulomb…
We consider Schr\"odinger operators on [0,\infty) with compactly supported, possibly complex-valued potentials in L^1([0,\infty)). It is known (at least in the case of a real-valued potential) that the location of eigenvalues and resonances…
Quark-hadron duality is studied in a systematic way for both the unpolarized and polarized structure functions, by taking into account all the available data in the resonance region.In both cases, a detailed perturbative QCD based analysis…
The matter operator in the double-scaled SYK model exhibits special properties when its dimension is analytically continued to -1/2. At this dimension, the operator is in a degenerate representation of the q-deformed oscillator algebra and…
Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it…
Two planar supersymmetric quantum mechanical systems built around the quantum integrable Kepler/Coulomb and Euler/Coulomb problems are analyzed in depth. The supersymmetric spectra of both systems are unveiled, profiting from symmetry…
We study the threshold behaviour of two dimensional Schr{\" o}dinger operators with finitely many local point interactions. We show that the resolvent can either be continuously extended up to the threshold, in which case we say that the…
We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the…
We find the Courant-sharp Neumann eigenvalues of the Laplacian on some 2-rep-tile domains. In $\R^{2}$ the domains we consider are the isosceles right triangle and the rectangle with edge ratio $\sqrt{2}$ (also known as the A4 paper). In…