相关论文: Potential scattering in $L^2$ space: (2) Rigorous …
We consider the propagation of wave packets for a nonlinear Schr\"odinger equation, with a matrix-valued potential, in the semi-classical limit. For a matrix-valued potential, Strichartz estimates are available under long range assumptions.…
Scattering and electron-positron pair production by a one-dimensional potential is considered in the framework of the $S-$matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogoliubov…
We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally…
A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging or communication purposes.…
The behavior of a twisted electron colliding with a linearly polarized laser pulse is investigated within relativistic quantum mechanics. In order to better fit the real experimental conditions, we introduce a Gaussian spatial profile for…
A particle initially in a pure state but interacting with some environment evolves into a discrete ensemble of pure states, the eigenstates of its reduced density operator, with ensemble probabilities given by the corresponding eigenvalues.…
In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified…
We analyze oscillations of intermediate neutrinos in terms of the scattering of particles described by Gaussian wave packets. We study a scalar model as in a previous paper (I) but in realistic situations, where the two particles of the…
We consider scattering of a free quantum particle on a singular potential with rather arbitrary shape of the support of the potential. In the classical limit $\hbar=0$ this problem reduces to the well known problem of chaotic scattering.…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
We study the quantum entanglement produced by a head-on collision between two gaussian wave packets in three-dimensional space. By deriving the two-particle wave function modified by s-wave scattering amplitudes, we obtain an approximate…
We derive statistical distributions for the degrees of freedom in wave packet molecular dynamics models. Specifically, a theory is developed for the width distributions of Gaussian wavepackets in both isotropic and anisotropic formulations.…
We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially…
Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with…
We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value…
In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable nonlinear parameter $A$ upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of…
The theory of acoustic wave scattering by many small bodies is developed for bodies with impedance boundary condition. It is shown that if one embeds many small particles in a bounded domain, filled with a known material, then one can…
We develop a formalism for computing the scattering amplitudes in maximally symmetric de Sitter spacetime with compact spatial dimensions. We describe quantum states by using the representation theory of de Sitter symmetry group and link…
The propagation of acoustic waves in a poro-elastic medium of infinite extension containing spherical cavities randomly distributed is investigated. The scattering coefficients are computed in the low frequency limit using the sealed pore…
We discuss some of the properties of the `collision' of a quantum mechanical wave packet with an infinitely high potential barrier, focusing on novel aspects such as the detailed time-dependence of the momentum-space probability density and…