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

Authors

• Kevin G. Hernandez * ¹
• Sergio E. Aguilar-Gutierrez * ^{1, 2}
• Jorge Bernalc ³

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

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