Related papers: Revisiting double Dirac delta potential
Dirac particles can undergo perfect transmission through a sufficiently high potential barrier in the Klein zone. Although the perfect Klein tunneling (often referred to as the Klein paradox) is similar to the non-relativistic resonant…
Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for…
We point out that a non-overlapping well (at negative energies) adjacent to a finite barrier (at positive energies) is a simple potential which is generally missed out while discussing the one-dimensional potentials in the textbooks of…
It is shown that a Dirac particle of mass $m$ and arbitrarily small momentum will tunnel without reflection through a potential barrier $V=U_c(x)$ of finite range provided that the potential well $V=-U_c(x)$ supports a bound state of energy…
Recently, the non-zero transmission of a quantum particle through the one-dimensional singular potential given in the form of the derivative of Dirac's delta function, $\lambda \delta'(x) $, with $\lambda \in \R$, being a potential strength…
For potential barriers with scalar and vector coupling, we show that a Dirac particle could experience nearly full transmission within a wide sub-barrier energy band. Moreover, for certain potential configurations, including pseudo-spin…
The double-well problem for the two-dimensional Dirac equation is solved for a family of quasi-one-dimensional potentials in terms of confluent Heun functions. We demonstrate that for a double well separated by a barrier, both the energy…
The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrodinger's equation with generalized…
For an asymmetric double-well potential system, it is shown that, if the potential is quadratic until it reaches several times of the zero-point energies from the bottoms in each well, the energy eigenvalues of the low lying excited states…
We review the analytic results for the phase shifts delta_{l}(k) in non-relativistic scattering from a spherical well. The conditions for the existence of resonances are established in terms of time-delays. Resonances are shown to exist for…
Usually, the reflection probability $R(E)$ of a particle of zero energy incident on a potential which converges to zero asymptotically is found to be 1: $R(0)=1$. But earlier, a paradoxical phenomenon of zero reflection at zero energy…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
The two-component approach to the one-dimensional Dirac equation is applied to the Woods-Saxon potential. The scattering and bound state solutions are derived and the conditions for a transmission resonance (when the transmission…
We revisit a rectangular barrier as well as a rectangular well (pit) between two rigid walls. The former is the well known double-well potential and the latter is a hole potential. Let $|V_0|$ be the height (depth) of the barrier (well)…
We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches…
We obtain exact scattering solutions of the Dirac equation in 1+1 dimensions for a double square barrier vector potential. The potential floor between the two barriers is higher than 2mc^2 whereas the top of the barriers is at least 2mc^2…
We report on several new basic properties of a parabolic dot in the presence of a magnetic field. The ratio between the potential strength and the Landau level (LL) energy spacing serves as the coupling constant of this problem. In the weak…
The spherically symmetric potential $a \,\delta (r-r_0)+b\,\delta ' (r-r_0)$ is generalised for the $d$-dimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac…
We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domain-wise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard…
The resonant transmission of a moving particle which interacts with an one-dimensional array of N delta-function potentials is investigated. A suitable transfer matrix formulation is used to obtain the particle transmission. We give the…