相关论文: The (2+1) Dirac Equations with $\delta$ Potential

The bound state solution of Coulomb Potentials in the Dirac equation is calculated for position dependent mass function M(r) within the framework of asymptotic iteration method (AIM). The eigenfunctions are derived in terms of…

A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term…

Dirac delta-function potential is widely studied in quantum mechanics because it usually can be exactly solved and at the same time is useful in modeling various physical systems. Here we study a system of delta-potential trapped spinorbit…

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…

There is much discussion in the mathematical physics literature as well as in quantum mechanics textbooks on spherically symmetric potentials. Nevertheless, there is no consensus about the behavior of the radial function at the origin,…

We study the two-dimensional massless Dirac equation for a potential that is allowed to depend on the energy and on one of the spatial variables. After determining a modified orthogonality relation and norm for such systems, we present an…

The solution of the Dirac equation for an attractive linear potential is considered. The Lorentz nature of the potential (vector or scalar) affects the existence of bound states. For simplicity, and since it is sufficient for the goals of…

The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…

We extend Panella and Roy's [13] work on one-dimensional heterostructure for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where both the mass and velocity are position-dependent. Bound states…

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…

A superspace version of the Schr\"odinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension M in case M is…

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for…

Levinson's theorem for the Dirac equation is known in the form of a sum of positive and negative energy phase shifts at zero momentum related to the total number of bound states. In this letter we prove a stronger version of Levinson's…

In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…

The problem of a fermion subject to a convenient mixing of vector and scalar potentials in a two-dimensional space-time is mapped into a Sturm-Liouville problem. For a specific case which gives rise to an exactly solvable effective modified…

One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets)…

The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector-scalar-pseudoscalar square potentials, the states of relativistic fermions are investigated. This…

In this paper we consider bound state solutions, i.e., normalizable time-periodic solutions of the Dirac equation in the exterior region of an extreme Kerr black hole with mass $M$ and angular momentum $J$. It is shown that for each…

A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part…