Effects of position-dependent mass (PDM) on the bound-state solutions of a massive spin-0 particle subjected to the Yukawa potential

2024/11/05 by Oliveira, P. H. F., Lima, W. P.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2411.02690

Abstract

With the advent of Albert Einstein's theory of special relativity, Klein and Gordon made the first attempt to elevate time to the status of a coordinate in the Schrödinger equation. In this study, we graphically discuss the eigenfunctions and eigenenergies of the Klein-Gordon equation with a Yukawa-type potential (YP), within a position-dependent mass (PDM) framework. We conclude that the PDM leads to the equivalence of the positive (E⁺) and negative (E^-) solution states at low energies. We observe that in the energy spectrum as a function of η (YP intensity factor), the PDM can induce gap closure at the critical point where E⁺ and E^- become imaginary. In the spectrum as a function of α (YP shielding factor), it can compel the energies to be zero at α=0, instead of being equal to (m₀c²) as in the invariant mass case.

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