# Solution of the $\kappa$-deformed Dirac equation with vector and scalar interactions in the context of spin and pseudospin symmetries

## TL;DR

This paper explores the effects of quantum deformation on the Dirac equation with vector and scalar interactions, analyzing energy spectra and wave functions under spin and pseudospin symmetries in various physical systems.

## Contribution

It introduces a $$-deformed Dirac equation framework incorporating minimal and scalar couplings, revealing how quantum deformation influences physical phenomena and particle properties.

## Key findings

- Deformation parameter modifies energy eigenvalues and wave functions.
- Linear potential induces Coulomb-like terms in the equation.
- Quantum deformation affects spin-dependent properties.

## Abstract

The deformed Dirac equation invariant under the $\kappa$-Poincar\'{e}-Hopf quantum algebra in the context of minimal and scalar couplings under spin and pseudospin symmetries limits is considered. The $\kappa$-deformed Pauli-Dirac Hamiltonian allows us to study effects of quantum deformation in a class of physical systems, such as an Zeeman-like effect, Aharonov-Bohm effect and an anomalous-like contribution to the electron magnetic moment, between others. In our analysis, we consider the motion of an electron in a uniform magnetic field and interacting with (i) a planar harmonic oscillator and (ii) a linear potential. We verify that the particular choice of a linear potential induces a Coulomb-type term in the equation of motion. Expressions for the energy eigenvalues and wave functions are determined taking into account both symmetries limits. We verify that the energies and wave functions of the particle are modified by the deformation parameter as well as by the element of spin.