Semiclassical theory of potential scattering for massless Dirac fermions (original) (raw)
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Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional spacetime
Physics Letters A, 2003
The problem of scattering of neutral fermions in two-dimensional space-time is approached with a pseudoscalar potential step in the Dirac equation. Some unexpected aspects of the solutions beyond the absence of Klein´s paradox are presented. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength. Added plausibility for the existence of bound-state solutions in a pseudoscalar double-step potential found in a recent Letter is given.
The Journal of Chemical Physics, 1985
The semiclassical theory developed by Maslov and Fedoriuk is used to calculate the wave function for two-dimensional scattering from a Morse potential. The characteristic function S and the density Jacobian J are computed in order to obtain the primitive wave function. The incident part shows distorted plane-wave behavior and the scattered part shows radially outgoing behavior. A uniform approximation gives a wave function that is well behaved near the caustic. H [BK: pO(qO), q~ = E.
Scattering problems involving electrons, photons, and Dirac fermions
2008
Prof. dr. J. M. van Ruitenbeek Prof. dr. ir. W. van Saarloos Dr. J. Tworzydło (Universiteit van Warschau) Prof. dr. J. Zaanen Dit werk maakt deel uit van het onderzoekprogramma van het Stichting voor Fundamenteel Onderzoek der Materie (FOM), die financieel wordt gesteund door de Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).
On the Dirac Scattering Problem
We consider a method of solving the Dirac scattering problem based on an approach previously used by the authors to solve the Schrödinger scattering problem to develop a conditional exact scattering solution and an unconditional series solution. We transform the Dirac scattering problem into a form that facilitates a solution based on the relativistic Lippmann-Schwinger equation using the relativistic Green's function that is transcendental in terms of the scattered field. Using the Dirac operator, this solution is transformed further to yield a modified relativistic Lippmann-Schwinger equation that is also transcendental in terms of the scattered field. This modified solution facilitates a condition under which the solution for the scattered field is exact. Further, by exploiting the simultaneity of the two solutions available, we show that is possible to define an exact (non-conditional) series solution to the problem.
Journal of Physics A: Mathematical and Theoretical, 2012
A methodology based on generalized Sturmian functions is put forward to solve two-and three-body scattering problems. It uses a spectral method which allows for the inclusion of the correct asymptotic behavior when solving the associated driven Schrödinger equation. For the two-body case, we demonstrate the equivalence between the exterior complex scaling (ECS) and the Sturmian approaches and illustrate the latter by using Hulthén Sturmian functions. Contrary to the ECS approach, no artificial cutoff of the potential is required in the Surmian approach. For the three-body scattering problem, the theoretical framework is presented in hyperspherical coordinates and a set of hyperspherical generalized Sturmian functions possessing outgoing asymptotic behavior is introduced. The Sturmian procedure is a direct generalization of the method discussed for the two-body problem; thus, the comparison with the ECS method is similar. For both the two-and three-body cases, Sturmian bases are efficient as they possess the correct outgoing behavior, diagonalize part of the potentials involved and are essentially localized in the region where the unsolved interaction is not negligible. Moreover, with the Sturmian basis, the operator (H − E) is represented by a diagonal matrix whose elements are simply the Sturmian eigenvalues.
Scattering by one-dimensional smooth potentials: between WKB and Born approximation
The paper discusses the applicability of WKB and Born (small perturbations) approximations in the problem of the backscattering of quantum particles and classical waves by one-dimensional smooth potentials with small amplitudes compared to the energy of the incident particle (above-barrier scattering). Both deterministic and random potentials are considered. The dependence of the reflection coefficient and localization length on the amplitude and the longitudinal scale of the scattering potential is investigated. It is shown that perturbation and WKB theories are inconsistent in the above-barrier backscattering problem. Not only the solutions but the regions of validity of both methods as well depend strongly on the details of the potential profile, and are individual for each potential. For deterministic potentials, a simple criterion that allows determining the boundary between the applicability domains of WKB and Born approximations is found. r
On scattering from the one-dimensional multiple Dirac delta potentials
European Journal of Physics
In this paper, we propose a pedagogical presentation of the Lippmann-Schwinger equation as a powerful tool so as to obtain important scattering information. In particular, we consider a one dimensional system with a Schrödinger type free Hamiltonian decorated with a sequence of N attractive Dirac delta interactions. We first write the Lippmann-Schwinger equation for the system and then solve it explicitly in terms of an N × N matrix. Then, we discuss the reflection and the transmission coefficients for arbitrary number of centers and study threshold anomaly for N = 2 and N = 4 cases. We also study further features like quantum metastable states like resonances, including their corresponding Gamow functions, and virtual or antibound states. The use of the Lippmann-Schwinger equation simplifies enormously our analysis and gives exact results for an arbitrary number of Dirac delta potential.
Advances in High Energy Physics, 2017
In this paper, we studied the approximate scattering state solutions of the Dirac equation with the hyperbolical potential with pseudospin and spin symmetries. By applying an improved Greene-Aldrich approximation scheme within the formalism of functional analytical method, we obtained the spin-orbit quantum numbers dependent scattering phase shifts for the spin and pseudospin symmetries. The normalization constants, lower and upper radial spinor for the two symmetries, and the relativistic energy spectra were presented. Our results reveal that both the symmetry constants (Cps and Cs) and the spin-orbit quantum number κ affect scattering phase shifts significantly.
Quantum scattering of particles by one-dimensional constant potential
2018
The behaviour and state of electron-particles in a crystal lattice was determined by plotting Dirac-Kronig Penney model of actual scattering power and varied scattering power on MAPLE. Numerical analysis was done on the actual and varied model by writing a FORTRAN code that uses Newton-Raphson (taking initial guess for the code from MAPLE graphs band) to output their various plane waves . Their various plane waves were used to calculate their free energy particles E for both actual and varied model which was then plotted on MATLAB to give the description of the Energy spectrum of crystals.