On the correspondence principle for the Klein-Gordon and Dirac Equations
الموضوعات : Journal of Theoretical and Applied Physics
Kevin Hernandez
1
(Department of Physics, University of El Salvador, Ciudad Universitaria, San Salvador, El Salvador)
Sergio Ernesto Aguilar Gutierrez
2
(Instituut voor Theoretische Fysica, K.U. Leuven, Leuven, Belgium|Department of Physics, University of El Salvador, Ciudad Universitaria, San Salvador, El Salvador)
Jorge Bernal
3
(División Académica De Ciencias Básicas, Universidad Juárez Autónoma de Tabasco,
Cunduacán, Tabasco, México)
الکلمات المفتاحية: Quantum foundations, Classical transition, Relativistic wave equations,
ملخص المقالة :
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.
