相关论文: New exactly solvable periodic potentials for the D…

We study the Dirac equation in 3+1 dimensions with non-minimal coupling to isotropic radial three-vector potential and in the presence of static electromagnetic potential. The space component of the electromagnetic potential has angular…

We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.

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…

It has been observed that a quantum theory need not to be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many complex potentials, and we obtain the real relativistic energy eigenvalues and…

A single spin-$\frac{1}{2}$ particle obeys the Dirac equation in $d\ge 1$ spatial dimension and is bound by an attractive central monotone potential which vanishes at infinity (in one dimension the potential is even). This work refines the…

Solutions of the one dimensional Dirac equation with piece-wise constant potentials are presented using standard methods. These solutions show that the Klein Paradox is non-existent and represents a failure to correctly match solutions…

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary transformation and shown to…

We obtain the energy eigenvalues and radial wave functions of the D-Dimensional Dirac equation in the case of spin symmetry for Woods-Saxon potential in minimal length formalism. The radial part of the D-Dimensional Dirac equation is solved…

The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into…

We discuss, in a pedagogical way, how to solve for relativistic wave functions from the radial Dirac equations. After an brief introduction, in Section II we solve the equations for a linear Lorentz scalar potential, V_s(r), that provides…

We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional P\"oschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the…

We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…

In the present work we establish a simple relation between the Dirac equation with a scalar and an electromagnetic potentials in a two-dimensional case and a pair of decoupled Vekua equations. In general these Vekua equations are bicomplex.…

We investigate two methods of obtaining exactly solvable potentials with analytic forms.

A new family of solvable potentials related to the Schroedinger-Riccati equation has been investigated. This one-dimensional potential family depends on parameters and is restricted to the real interval. It is shown that this potential…

Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…

We generalize the original derivation of transparent, static Schroedinger potentials by Kay and Moses, to obtain a large class of time-dependent transparent Dirac potentials in one spatial dimension. They contain all known transparent…

Approximate solutions of the Dirac equation are found for ultrarelativistic particles moving in a periodic potential, which depends only on one coordinate, transverse to the largest component of the momentum of the incoming particle. As an…

Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be…

There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…