Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential

Abstract

The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb 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. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and ${\gamma }^5$ chiral transformations. The cases of pure pseudoscalar and mixed vector-scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions.

arXiv comment11 pages, 5 figures (Ann. Phys.)

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• Fermions in the background of mixed vector-scalar-pseudoscalar square potentials
• Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics