Dirac equation with complex potentials

Abstract

We study (2 + 1) dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another class of potentials zero energy solutions can be obtained analytically. For the scalar potential cases, it has also been shown that the effective Schrödinger-like equations resulting from decoupling the spinor components can be interpreted as exactly solvable energy dependent Schrödinger equations.

Coherent states for graphene under the interaction of crossed electric and magnetic fields

“…[14][15][16][17][18][19]). Nevertheless, when an electric field interacts with the above system the problem nature changes, so that it is necessary to implement either a numerical method or a process that involves rotations in order to solve the equations that appear [19][20][21][22][23]. For instance, for position-dependent electrostatic potentials U (x), a relativistic approach is often used to become the problem into an analogous one of special relativity with a massless particle moving with an effective velocity v F [24][25][26].…”

The massless Dirac–Weyl equation with deformed extended complex potentials

“…Graphene has got a honeycomb structure with a single layer of carbon atoms is a two dimensional material. Then, the study of Dirac-Weyl particles in magnetic fields has received much attention for confining the charges [2], [3], [4], [5]. Moreover, the Dirac theory in low dimensions is studied for the different potentials both numerically [6] and theoretically [7], [8].…”

Time-dependent massless Dirac fermions in graphene

“…Especially the Dirac equation in the presence of a magnetic field is of great interest as, unlike electrostatic potentials, such a configuration allows in principle to confine the Dirac fermions [4,5,6]. Many exact solutions have been provided for a variety of time-independent Hamiltonians and magnetic field configurations [7,8,9], including some for complex magnetic fields leading to pseudo/quasi-Hermitian interactions [10,11]. While some solutions for the time-dependent Dirac equation in 1+1 dimensions have been constructed [12,13,14], little is known about the time-dependent setting with a magnetic field in 2+1 dimensions and no exact solutions have been reported.…”