On Relativistic Transmissions through a Symmetrical Pair of Delta-Barriers or Delta-Wells

Abstract

73.40.Gk The solution of the one-dimensional Dirac equation is examined for the symmetrical double deltafunction potential. A formula for the relativistic transmission coefficient is derived from the solution. The maximum condition as well as the minimum condition for the transmission coefficient is determined. The transmission coefficient is shown to be equal to unity in its maximum. In its minimum, it is smaller than the transmission coefficient for the single delta-function potential of the twofold strength. Further, some differences between the relativistic and non-relativistic transmission coefficient are presented. It is found that the wave numbers, at which the maxima and minima occur according to the non-relativistic treatment, are shifted by the relativistic treatment. Unlike the non-relativistic transmission coefficient, the relativistic transmission coefficient does not approach unity in the range of high energies. It oscillates between unity and a constant. The value of this constant depends on the strength of the delta-interaction. Thus, the relativistic corrections to the transmission coefficient for the symmetrical double delta-function potential are found to represent significant shifts in its characteristics.

Relativistic Stark resonances in a simple exactly soluble model for a diatomic molecule

“…Once the Weyl-Titchmarsh functions are known, it is straightforward to compute the spectral density using (19), (109) and (110). It is a complicated functions of the interatomic distance R, the potential strength g and the electric field strength F .…”

“…Using these ideas, we derive in the appendix a family of boundary conditions consistent with (A. 19), and thus having the right mathematical properties (self-adjointness and non-relativistic limit). From this analysis, the following boundary conditions are obtained:…”

“…This kind of simplified models using point-like interaction has been studied extensively both relativistically [14][15][16][17][18][19] and non-relativistically [20,21] for scattering and bound states problems when the electric field is absent. In these cases, an analytical solution can be calculated easily.…”

Transmission Properties of the One-Dimensional Array of Delta Potentials

“…The problem of one-dimensional delta-function potential array has been studied in previus works 13,14,15,16,17 . In reference 13 they use a field-theoretic approach to obtain the transfer matrix in terms of a propagator.…”

“…The problem of one-dimensional delta-function potential array has been studied in previus works 13,14,15,16,17 . In reference 13 they use a field-theoretic approach to obtain the transfer matrix in terms of a propagator. In references 14,15,16,17 the case of two delta-function potentials is studied using a quantum-mechanical approach. We use a similar aproach to develop a convenient way to deal with the problem, based in a transfer matrix methodology.…”