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

محورهای موضوعی : Journal of Theoretical and Applied Physics

Kevin Hernandez ¹ , Sergio Ernesto Aguilar Gutierrez ² , Jorge Bernal 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|Department of Physics, University of El Salvador, Ciudad Universitaria, San Salvador, El Salvador
3 - División Académica De Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Cunduacán, Tabasco, México

تاریخ دریافت : 1401/05/31 تاریخ پذیرش : 1401/07/24 تاریخ انتشار : 1401/09/10

کلید واژه: Quantum foundations, Classical transition, Relativistic wave equations,

چکیده مقاله :

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.