Fermions in the background of mixed vector–scalar–pseudoscalar square potentials

Abstract

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 relativistic problem can be mapped into a effective Schrödinger equation for a square potential with repulsive and attractive delta-functions situated at the borders. An oscillatory transmission coefficient is found and resonant state energies are obtained. In a special case, the same bound energy spectrum for spinless particles is obtained, confirming the predictions of literature. We showed that existence of bound-state solutions are conditioned by the intensity of the pseudoscalar potential, which posses a critical value.

Quantum dynamics of relativistic bosons through nonminimal vector square potentials

“…The energy bound states were obtained in a simple way from the poles of transmission amplitude. The parity of bound solutions is broken, similar to the fermions problem in the same potential which was already discussed in the literature [22]. The bound states spectrum reveals the Schiff-Snyder-Weinberg effect [32], confirming the Popov's work [33] and its applicability to the DKP formalism.…”

“…Additionally, we obtain the energy spectrum of bound states by a simple and transparent way. We show that the eigenenergies obtained have great similarity to the problem of fermions in the same potential, already explored in the literature [22].…”

“…Another expected result is T → 1 when E → ±∞, observed in the figure 1 (logically, there is a symmetry E → −E ). We can observe a great similarity between T for fermions [22] and bosons in the same potential, i.e, both do not depend on delta function localization and have the same resonance points. This is well understood because both have the same effective Schrödinger equations for spinor components in square potentials.…”

“…As expected, there are bound state solutions just for j < 0 and b 1 = 1, because the effective equation show a attractive potential between the two delta function potentials. It is like fermions bind by the same effective potential [22].…”

Dirac Hamiltonian in a supersymmetric framework

“…Here the idea of the pseudospin symmetry (see, for example, [8]) turned out to be fruitful in understanding the degeneracies of orbitals in a single particle spectra in a relativistic mean field setting. The mean field was supposed to be an artifact of the presence of vector and scalar potentials [9,10]. Apart from SQM, some of the other methods towards seeking exact solutions of the Dirac equation include the separation of variable method and the noncommutative integration method (see [11] and references therein).…”