Related papers: Wave packets in quantum theory of collisions
The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal…
We develop a statistical theory describing quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of systems, ranging from atomic…
We use a three-body Continuum Discretized Coupled Channel (CDCC) model to investigate Coulomb and nuclear effects in breakup and reaction cross sections. The breakup of the projectile is simulated by a finite number of square integrable…
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…
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…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
The interaction of a wave packet (and in particular the wave front) with a mass barrier is investigated in one dimension. We discuss the main features of the wave packet that are inherent to two-dimensional wave packets, such as compression…
The collision of a quantum Gaussian wave packet with a square barrier is solved explicitly in terms of known functions. The obtained formula is suitable for performing fast calculations or asymptotic analysis. It also provides physical…
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…
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…
In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a…
In this paper we discuss some aspects of the theory of wave packets. We consider a popular non-covariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic…
We develop a new variant of the wave-packet analysis and solve the tunneling time problem for one particle. Our approach suggests an individual asymptotic description of the quantum subensembles of transmitted and reflected particles both…
In this paper, we propose an approach based on the theory of an axiomatic $S$ matrix and partially switching on an interaction, which is extremely suitable for describing the phenomenon of oscillations within the framework of quantum field…
These lectures treat scattering theory from a non-perturbative point of view. The course begins with a review of formal aspects in scattering theory, discussing the in/out states and the $S$ matrix that connects them. Unitarity relations,…
Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and…
We consider the problem of quantum scattering of a localized wave packet by a weak Gaussian potential in two spatial dimensions. We show that, under certain conditions, this problem bears close analogy with that of focusing (or defocusing)…
For matter wave scattering from passive quantum obstacles, we propose a phase diagram in terms of phase and modulus of scattering coefficients to explore all possible directional scattering patterns. In the phase diagram, we can not only…
We present a multiscale quantum-defect theory (QDT) for two identical atoms in a symmetric harmonic trap that combines the quantum-defect theory for the van der Waals interaction [B. Gao, Phys. Rev. A \textbf{64}, 010701(R) (2001)] at short…