Related papers: Analyses of reflection and transmission at moving …
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
We study the one dimensional time dependent Schr\"{o}dinger equation for a potential step with $E < V_0$. We obtain the wave is not instantaneously reflected, but for a few moment of time the wave packet penetrate into inaccessible…
We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model…
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,…
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast,…
People are familiar with quantum mechanical reflection and transmission coefficient. In all those cases corresponding potentials are usually assumed as of constant height and depth. For the cases of varying potential, corresponding…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
We show that an incident wavepacket at the boundary to a medium with extremely slow group velocity, experiences enhanced reflection and a substantial spatial and temporal distortion of the transmitted wave packet. In the limit of vanishing…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
This paper continues the preceding paper on the problem of quantum dynamics on the lattice. Firstly we consider the multiple reflections of the wave function (Loschmidt echo). The phenomenon of wave function concentration on the impurity…
A complete one-dimensional scattering of a spinless particle on a time-independent potential barrier is considered. To describe separately transmitted and reflected particles in the corresponding subsets of identical experiments, we…
In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential…
We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection…
The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically…
We analyze the matter wave transmission above a step potential within the framework of the cubic-nonlinear Schr\"odinger equation. We present a comprehensive analysis of the corresponding stationary problem based on an exact second-order…
In this paper we study the joint distributions of the telegraph process and its maximum conditioned on the number of changes of direction and the initial velocity. We prove that in the case of positive starting velocity, a form of the…
In this note we use the notion of time-delay to explain the physical content of the transformation properties of transmission and reflection amplitudes, as a result of a displacement of the potential. Then, we reconsider the recent analysis…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type…