Related papers: One-dimensional quantum scattering by a parabolic …
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
We consider non-linear Schr\"odinger equations with a potential, and non-local non-linearities, that are models in mesoscopic physics, for example of a quantum capacitor, and that also are models of molecular structure. We study in detail…
We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising…
In this paper, we provide the two-body exact solutions of two dimensional (2D) Schr\"{o}dinger equation with isotropic $\pm 1/r^3$ interactions. Analytic quantum defect theory are constructed base on these solutions and are applied to…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
The scattering of wave packets from a single slit and a double slit with the Schr\"odinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region,…
Scattering of charged particles is ubiquitous in nuclear physics. We calculate the proton-proton $s$-wave phase shift at low energy relevant to solar physics. The phase shift is calculated from the ratio of the regular and irregular…
This study concerns the two-body scattering of particles in a one-dimensional periodic potential. A convenient ansatz allows for the separation of center-of-mass and relative motion, leading to a discrete Schr\"odinger equation in the…
We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…
In the paper the one-dimensional one-center scattering problem with the initial potential $\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as…
In the standard Breit-Wigner approach to scattering the phase shift is to have a form $\tan\delta_{\rm BW} =\Gamma_1/(E_1-E)$ at a real energy resonance. This leads to complex energy poles in the scattering amplitude at $E_{\rm…
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…
The quantum-mechanical scattering on a compact Riemannian manifold with semi-axes attached to it (hedgehog-shaped manifold) is considered. The complete description of the spectral structure of Schroedinger operators on such a manifold is…
Scattering of a scalar particle on a crystalline plane with quadratic cell and identical fixed scatterers is solved precisely. Contradiction of the standard scattering theory is pointed out.
The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension $d\geq3$, we introduce a stationary scattering theory for Schr\"odinger operators which is regular at zero energy.…
We consider the three-dimensional cubic nonlinear Schr\"odinger system \begin{equation*} \begin{cases} i\partial_tu+\Delta u+(|u|^2+\beta |v|^2)u=0,\\ i\partial_tv+\Delta v+(|v|^2+\beta |u|^2)v=0. \end{cases} \end{equation*} Let $(P,Q)$ be…
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
We study the inverse scattering problem for the three dimensional nonlinear Schroedinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of…
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…