Related papers: On Scattering of 1-D Wave Packets
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
The standard scattering theory (SST) in non relativistic quantum mechanics (QM) is analyzed. Self-contradictions of SST are deconstructed. A direct way to calculate scattering probability without introduction of a finite volume is…
A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…
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 problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…
We discuss "the plane wave approximation" to quantum mechanical scattering using simple one-dimensional examples. The central points of the paper are that (a) plane waves should be thought of as infinitely wide wave packets, and (b) the…
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,…
A numerical approach to the problem of wave scattering by many small particles is developed under the assumptions k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. On the wavelength…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
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.
Normalized wave packets express particles in nature. Their sizes are determined by their interactions with matter, and depend on environments. Nevertheless, these characterize scatterings processes in realistic situations, and govern the…
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 calculate the quantum states of regular polygons made of 1D quantum wires treating each polygon vertex as a scatterer. The vertex scattering matrix is analytically obtained from the model of a circular bend of a given angle of a 2D…
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…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
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.
We propose a novel approach for solving the scattering of light onto a two-level atom coupled to a one-dimensional waveguide. We first express the physical quantity of interest in terms of Feynman diagrams and treat the atom as a…
We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher…
Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…