Quasi-relativistic description of a quantum particle moving through one-dimensional piecewise constant potentials

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Abstract

Using a novel quasi-relativistic wave equation, which can give precise results up to energies ~mc2, exact quantum mechanical solutions are found which corresponds to a particle with mass moving through one-dimensional piecewise constant potentials. As expected, at low particle's speeds, the found solutions coincide with the solutions of the same problems calculated using the Schrödinger equation; however, as it should be, both solutions have a significative difference at quasi-relativistic speeds. Then, it is argued that the quasi-relativistic wave equation provides a simpler description than a fully relativistic theory or the perturbation approach for a quantum particle moving at quasi-relativistic energies through piecewise constant potentials.

Original languageEnglish
Article number103318
JournalResults in Physics
Volume18
DOIs
StatePublished - Sep 2020

Keywords

  • Quantum mechanics
  • Relativistic quantum mechanics

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