Related papers: Quantum scattering with semiclassical asymptotic m…
The precise connection between quantum wave functions and the underlying classical trajectories often is presented rather vaguely by practitioners of quantum mechanics. Here we demonstrate, with simple examples, that the imaging theorem…
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
The article discusses the correctness of the assumption about the similarity of molecular continuum electron functions with wave functions in electron-atom scattering. The elastic scattering of slow particles by pair of non-overlapping…
Unbound wave packets propagating to macroscopic space and time coordinates become proportional to their (Fourier transform) momentum distribution at earlier times whereby the asymptotic coordinates and the initial momenta are connected…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
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 present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
In the paper, we discuss the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. In the previous works it is shown that in these models of classical…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of…
Quantum Rutherford scattering and scattering of classical waves off Coulomb-like potentials have similar formal structures and can be studied using the same mathematical techniques. In both contexts, the long-range nature of the interaction…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…
We consider a fully quantized model of spontaneous emission, scattering, and absorption, and study propagation of a single photon from an emitting atom to a detector atom both with and without an intervening scatterer. We find an exact…