(1+1)-Dimensional Dirac Equation With Non-Hermitian Interaction

Abstract

We study (1 + 1) dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.

Computer simulation of two continuous spin models using Wang–Landau-Transition-Matrix Monte Carlo algorithm

“…The error which is present in the density of states has been predicted to be proportional to ln f as is apparent from the theoretical work of Zhou and Bhatt [29]. This has been tested for a number of discrete and continuous models and the prediction has been found to be correct [30,31].…”

Relativistic Confinement of Neutral Fermions with Partially Exactly Solvable and Exactly Solvable PT-Symmetric Potentials in the Presence of Position-Dependent Mass

“…3 A plot of the symmetric mass distribution (29) where the effective energyẼ is defined asẼ = E 2 − M 2 0 . Equation (31) shows that the position-dependent effective mass Dirac equation with the PT-symmetric Lorentz vector potential (30) can be mapped into the Schrödinger-like equation with the exactly solvable modified Pöschl-Teller potential in 1 + 1 dimensions. The solution of the relativistic problem can be obtained from a comparison with the non-relativistic solution of the modified Pöschl-Teller potential problem treated, for instance, in the reference [64].…”

Effective Mass and Pseudoscalar Interaction in the Dirac Equation with Woods–Saxon Potential

“…[23], scattering solutions of the Dirac equation with PDM have been studied using the J-matrix method. By extending PT-symmetric quantum mechanics to the relativistic theory with PDM, several contributions have emerged in the literature, that investigate the Dirac equation for particles interacting with PT-symmetric potentials in the presence of PDM [32][33][34][35][36][37][38].…”