相关论文: Explicit solution for a Gaussian wave packet impin…
We build Gaussian wave packets for the linear Schr\"odinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in Ignat, Zuazua,…
Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the classical…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
A simple formula for the scattering of wave packets from a square well at long times is derived. The expression shows that the phenomenon of wave packet diffraction in space and time exists in three dimensions also. An experiment for the…
We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a ``canonical initial slope" for…
A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
The physical properties of electromagnetic waves in the presence of a gravitational plane wave are analyzed. Formulas for the Stokes parameters describing the polarization of light are obtained in closed form. The particular case of a…
A simple method is presented which enables us to construct scalar field solutions from any given Einstein-Maxwell solution in colliding plane waves. As an application we give scalar field extensions of the solution found by Hogan, Barrabes…
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has mass and charge density distributing in space,…
Due to a transient quantum interference during a wavepacket collision with a potential barrier, a particular momentum, that depends on the potential parameters but is close to the initial average momentum, becomes suppressed. The hole left…
We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The…
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…
Solutions of quaternionic quantum mechanics (QQM) are difficult to grasp, even in simple physical situations. In this article, we provide simple and understandable free particle quaternionic solutions, that can be easily compared to complex…
We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position…
The quantum scattering by smooth bodies is considered for small and large values of $kd$, with $k$ the wavenumber and $d$ the scale of the body. In both regimes, we prove that the forward scattering exceeds the backscattering. For high $k$,…
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…
Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the…
The main aim of this article is to discuss characteristic physical phenomena which govern the destruction of quantum coherence of material wave packets.
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…