Relativistic Effects of Mixed Vector-Scalar-Pseudoscalar Potentials for Fermions in 1+1 Dimensions

TL;DR

This paper investigates the bound-state solutions of fermions in 1+1 dimensions under mixed vector, scalar, and pseudoscalar potentials, revealing how different potential signs affect fermion and antifermion states.

Contribution

It provides a comprehensive analysis of fermions with combined potentials, including new solutions and insights into the effects of potential sign variations.

Findings

Bound-state solutions depend on potential sign combinations.

Special cases recover known Pöschl-Teller and kink-like potentials.

Results clarify fermion-antifermion differences in these potentials.

Abstract

The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar P\"{o}schl-Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases.