Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

Abstract

The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, $V_v+V_s=\mathrm{constant}$. These intrinsically relativistic and isospectral problems are solved in a case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.

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Cited by in corpus (8)

• Scattering and bound states of Dirac Equation in presence of cosmic string for Hulthén potential
• Fermion localization on two-field thick branes
• Fermion localization on branes with generalized dynamics
• Remarks on the Dirac oscillator in $(2+1)$ dimensions
• Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential
• Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings
• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Stationary states of fermions in a sign potential with a mixed vector-scalar coupling