10.30495/JTAP.162244

On the correspondence principle for the Klein-Gordon and Dirac Equations

PDF HTML
  • Kevin G. Hernandez1,
  • Sergio E. Aguilar-Gutierrez*2,
  • Jorge Bernalc3,
  1. Department of Physics, University of El Salvador, Ciudad Universitaria, San Salvador, El Salvador
  2. Instituut voor Theoretische Fysica, K.U. Leuven, Leuven, Belgium
  3. Division Academica De Ciencias Basicas, Universidad Juarez Autonoma de Tabasco, Cunduacan, Tabasco, Mexico
Cover Image

Published in Issue 2023-11-17

How to Cite

1.
Hernandez KG, Aguilar-Gutierrez SE, Bernalc J. On the correspondence principle for the Klein-Gordon and Dirac Equations. J Theor Appl phys. 2023 Nov. 17;16(4). Available from: https://oiccpress.com/jtap/article/view/1948
Crossref
Scopus
Google Scholar
Europe PMC

PDF views: 343

HTML views: 19

Abstract

We investigate the asymptotic behavior of the solutions to the Klein-Gordon and Dirac equations using the local spatial averaging approach to Bohr's correspondence principle in the large principal quantum number regime. The procedure is applied in two basic problems in $1+1$-dimensions, the relativistic quantum oscillator and the relativistic particle in a box. In the harmonic oscillator cases, we find that the corresponding probability densities reduce to their respective classical single-particle distributions plus a series of terms suppressed by powers of the $hbar$ constant, while particle in a box cases show a different structure for the quantum corrections.

Keywords

  • Classical transition,
  • Quantum foundations,
  • Relativistic wave equations
PDF HTML