Related papers: A Closed Formula for the Barrier Transmission Coef…
In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite 1D anisotropic periodic stratified media with an arbitrary number of cells. By invoking the…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the…
The simulation of quantum transport in a realistic, many-particle system is a nontrivial problem with no quantitatively satisfactory solution. While real-time propagation has the potential to overcome the shortcomings of conventional…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
For the stationary one-dimensional nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-) analytical approach. In…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
Quark deconfinement phase transition at finite temperature and density is investigated in the frame of quantum mechanics. By solving the Schr\"odinger equation for a heavy quark in a thermal mean field, we calculate the quark probability…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
We discuss electron scattering in a one-dimensional delta barrier potential with either time-dependent coupling constant (classical model) or a coupling constant that is linear in a boson coordinate (quantum model). We find an exact…
In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be…
In this paper we look at transmission through one-dimensional potential barriers that are piece wise constant. The Transfer Matrix approach is adopted and a new formula is derived for multiplying long matrix sequences that not only leads to…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
The dynamics near the top of a potential barrier is studied in the temperature region where quantum effects become important. The time evolution of the density matrix of a system that deviates initially from equilibrium in the vicinity of…
We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
If $\Psi$ is a quaternionic wave function, then $i\Psi\neq \Psi i$. Thus, there are two versions of the quaternionic Schr\"odinger equation (QSE). In this article, we present the second possibility for solving the QSE, following on from a…
A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A…
A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…