Related papers: Long-range potential scattering: Converting long-r…
Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a…
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a…
We extend the notion of the transfer matrix of potential scattering to a large class of long-range potentials $v(x)$ and derive its basic properties. We outline a dynamical formulation of the time-independent scattering theory for this…
Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the…
By large-distance asymptotics, in conventional scattering theory, at the cost of losing the information of the distance between target and observer, one arrives at an explicit expression for scattering wave functions represented by a…
We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma}. For 0 < gamma < or =1 we prove the…
We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
We study the theory of scattering for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling,in space dimension 3.We prove in particular the existence of modified wave operators for that system with…
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…
This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.
We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated…
The motion of two attractively interacting atoms in an optical lattice is investigated in the presence of a scattering potential. The initial wavefunction can be prepared by using tightly bound exact two-particle eigenfunction for vanishing…
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
A multi-channel scattering problem is studied from a point of view of integral equations system. The system appears while natural one-particle wave function equation of the electron under action of a potential with non-intersecting ranges…