Related papers: The Scattering amplitude for Newly found exactly s…
We apply a simple transformation method to construct a set of new exactly solvable potentials (ESP) which gives rise to bound state solution of $D$-dimensional Schr\"odinger equation. The important property of such exactly solvable quantum…
We introduce an algorithm for the solution of a system of radial Schr\"odinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…
A pair of scattering potentials are called $\alpha$-equivalent if they have identical scattering properties for incident plane waves with wavenumber $k\leq\alpha$ (energy $k^2\leq\alpha^2$.) We use a recently developed multidimensional…
The general formulas to calculate the phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are derived. It is shown that at asymptotically great distances from the target…
We study certain resonance-counting functions for potential scattering on infinite cylinders or half-cylinders. Under certain conditions on the potential, we obtain asymptotics of the counting functions, with an explicit formula for the…
The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature…
Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials. These potentials are shown to be shape…
Excited hadrons are seen as resonances in the scattering of lighter stable hadrons like $\pi$, $K$ and $\eta$. Many decay into multiple final states necessitating coupled-channel analyses. Recently it has become possible to obtain…
We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full…
We propose a simple, intuitive alternative method of deriving the rule for connecting asymptotic wave function amplitudes to scattering probabilities. This is illustrated using the standard example of a 1-D particle reflecting or…
Representation of the elastic scattering amplitude in the form of the path integral is obtained using the stationary Schroedinger equation. A few methods of evaluation of path integrals for large coupling constants are formulated. The…
Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in terms of X_m…
A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Pad\'e…
In this paper we introduce the concept of super periodic potential (SPP) of arbitrary order $n$, $n \in I^{+}$, in one dimension. General theory of wave propagation through SPP of order $n$ is presented and the reflection and transmission…
In this article we present a method to compute the scattering states of holes in spherical bands in the strong spin-orbit coupling regime. More precisely, we calculate scattering phase shifts and amplitudes of holes induced by defects in a…
We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.
This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero…