Related papers: Explicit solution for a Gaussian wave packet impin…
The tunneling of Gaussian wave packets has been investigated by numerically solving the one-dimensional Schr\"odinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier…
We consider multiple collisions of quantum wave packets in one dimension. The system under investigation consists of an impenetrable wall and of two hard-core particles with very different masses. The lighter particle bounces between the…
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…
We present an exact solution to the one-dimensional (1-D) scattering-from-a-barrier problem for an incident neutron described by a wave packet. As an aid to presenting our approach, we spend some time on a basic review of how wave packets…
Two methodological troubles of the quantum theory of collisions are considered. The first is the undesirable interference of the incident and scattered waves in the stationary approach to scattering. The second concerns the nonstationary…
An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother…
Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical…
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…
An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for…
We discuss some of the properties of the `collision' of a quantum mechanical wave packet with an infinitely high potential barrier, focusing on novel aspects such as the detailed time-dependence of the momentum-space probability density and…
The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check…
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)…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
A curious effect is uncovered by calculating the it time evolving probability of reflection of a Gaussian wave packet from a rectangular potential barrier while it is perturbed by reducing its height. A time interval is found during which…
Starting with a down to earth interpretation of quantum mechanics for a free particle, the disappearance and reappearance of interference in the 2 slit problem with a detector behind one are treated in detail. A partial interpretation of…
We consider time-dependent Gaussian wave packet solutions of the Schrodinger equation (with arbitrary initial central position, x_0, and momentum, p_0, for an otherwise free-particle, but with an infinite wall at x=0, so-called bouncing…
We present quasi-analytical and numerical calculations of Gaussian wave packet solutions of the Schr\"odinger equation for two-dimensional infinite well and quantum billiard problems with equilateral triangle, square, and circular…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an…
Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment.…