Related papers: Quantum scattering with semiclassical asymptotic m…
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…
We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for…
By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…
In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the exact result, is used to describe a scattering process. The…
A careful functional treatment of quantum scattering is given using Schwinger's dynamical principle which involves a functional differentiation operation applied to a generating functional written in closed form. For long range…
A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
This paper establishes an aspect of Bohr's correspondence principle, i.e. that quantum mechanics converges in the high frequency limit to classical mechanics, for commuting semiclassical unitary operators. We prove, under minimal…
We present a renewed wave-packet analysis based on the following ideas: if a quantum one-particle scattering process and the corresponding state are described by an indivisible wave packet to move as a whole at all stages of scattering,…
We develop a non-perturbative approach to simulating scattering on classical and quantum computers, in which the initial and final states contain a fixed number of composite particles. The construction is designed to mimic a particle…
We consider quantum scattering from a compactly supported potential $q$. The semiclassical limit amounts to letting the wavenumber $k \to \infty$ while rescaling the potential as $k^2 q$ (alternatively, one can scale Planck's constant…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
We theoretically investigate the quantum scattering of a single-photon pulse interacting with an ensemble of $\Lambda$-type three-level atoms coupled to a one-dimensional waveguide. With an effective non-Hermitian Hamiltonian, we study the…
Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This solves the long standing problem of quantizing the resonances and chaotic regions generically appearing in…
In conventional gravitational wave scattering theory, a large-distance asymptotic approximation is employed. In this approximation, the gravitational wave is approximated by its large-distance asymptotics. In this paper, we establish a…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
This paper describes an algorithmic system called SQT for the computer simulation of a wide class of quantum experiments on entangled particles. SQT maintains a hidden internal state for each particle and it provides an initialization…
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…
It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information…