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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 potential s 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.
We point out a misleading treatment in the recent literature regarding analytical solutions for nonminimal vector interaction for spin-one particles in the context of the Duffin-Kemmer-Petiau (DKP) formalism. In those papers, the authors use improper ly the nonminimal vector interaction endangering in their main conclusions. We present a few properties of the nonminimal vector interactions and also present the correct equations to this problem. We show that the solution can be easily found by solving Schr{o}dinger-like equations. As an application of this procedure, we consider spin-one particles in presence of a nonminimal vector linear potential.
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