TY - JOUR

T1 - Quasi-relativistic description of a quantum particle moving through one-dimensional piecewise constant potentials

AU - Grave de Peralta, Luis

N1 - Publisher Copyright:
© 2020 The Author

PY - 2020/9

Y1 - 2020/9

N2 - 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.

AB - 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.

KW - Quantum mechanics

KW - Relativistic quantum mechanics

UR - http://www.scopus.com/inward/record.url?scp=85089892027&partnerID=8YFLogxK

U2 - 10.1016/j.rinp.2020.103318

DO - 10.1016/j.rinp.2020.103318

M3 - Article

AN - SCOPUS:85089892027

VL - 18

JO - Results in Physics

JF - Results in Physics

SN - 2211-3797

M1 - 103318

ER -