Related papers: Application of the variational $R$-matrix method t…
One-body quantum tunneling to continuum is treated via the two-potential approach, dividing the tunneling potential into external and internal parts. We show that corrections to this approach can be minimized by taking the separation radius…
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 different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering…
A method of a non-stationary description of tunneling of a particle through the one-dimensional and spherically symmetric rectangular barriers on the basis of analisis of multiple internal reflections of wave packets in relation on the…
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the…
We study the tunneling zone solutions of a one-dimensional electrostatic potential for the relativistic (Dirac to Klein-Gordon) wave equation when the incoming wave packet exhibits the possibility of being almost totally transmitted through…
We present an analytical framework for studying quantum tunneling through multiple Dirac delta potential barriers in one dimension. Using the transfer matrix method, we derive a closed-form expression for the total transfer matrix of a…
A non-stationary method for tunneling description of non-relativistic particles and photons through a barrier on the basis of consideration of the multiple internal reflections of vawe packets in relation of barrier boundaries is presented.…
Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general…
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…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
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…
The quantum mechanical tunneling through multiple quantum barriers is a long-standing and well-known problem. Three methods proposed earlier to calculate the tunneling probabilities and energy splitting: (1). Instanton Method (2) WKb…
Electron-molecule collisions play a central role in both natural processes and modern technological applications, particularly in plasma processing. Conventional computational strategies such as the R-matrix method have been widely adopted…
Complex quantum trajectory approach, which arose from a modified de Broglie-Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft…
A new mechanism of tunnelling at macroscopic distances is proposed for a wave packet localized in one-dimensional disordered potential with mirror symmetry, V(-x)=V(x). Unlike quantum tunnelling through a regular potential barrier, which…
Quantum Computing is a rapidly developing field with the potential to tackle the increasing computational challenges faced in high-energy physics. In this work, we explore the potential and limitations of variational quantum algorithms in…
Using a recently developed procedure - multiple wave packet decomposition - here we study the phase time formulation for tunneling/reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties…
We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…