Related papers: Klein paradox and Scattering theory for the semi-c…
In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the…
The spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new…
The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the potential is strong enough. The vacuum charge…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We establish the scattering of solutions to the focusing mass supercritical nonlinear Schr\"odinger equation with a repulsive Dirac delta potential \[ i\partial_{t}u+\partial^{2}_{x}u+\gamma\delta(x)u+|u|^{p-1}u=0, \quad (t,x)\in {\mathbb…
The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the degrees of freedom of the target, the…
In this paper, we study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, we establish the existence and…
We investigate the scattering problem of a two-particle composite system on a delta-function potential. Using the time independent scattering theory, we study how the transmission/reflection coefficients change with the height of external…
The Dirac equation has been applied to fermions scattering from the downward potential step. The results show some particles do not fall off the edge of the step and reflect. Also, based on de Broglie-Bohm interpretation of quantum…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
The paper discusses the applicability of WKB and Born (small perturbations) approximations in the problem of the backscattering of quantum particles and classical waves by one-dimensional smooth potentials with amplitudes small compared to…
The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate…
We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…
We study the universal fluctuations of the Wigner-Smith time delay for systems which exhibit chaotic dynamics in their classical limit. We present a new derivation of the semiclassical relation of the quantum time delay to properties of the…
In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $\mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous…
On a Riemannian manifold with or without boundary, and whether bounded or unbounded, we consider a semilinear wave (or Klein-Gordon) equation with a subcritical nonlinearity (either defocusing or focusing). We establish local…
We consider the Dirac equation in cylindrically symmetric magnetic fields and find its normal modes as eigenfunctions of a complete set of commuting operators. This set consists of the Dirac operator itself, the $z$-components of the linear…
In this paper, we consider two types of the scattering problems (relativistic case), namely, the stationary scattering problem, where the distance $r$ tends to infinity, and the dynamical scattering problem, where the time $t$ tends to…