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

الموضوعات : 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

تاريخ الإرسال : 24 الإثنين , محرم, 1444 تاريخ التأكيد : 20 الأحد , ربيع الأول, 1444 تاريخ الإصدار : 07 الخميس , جمادى الأولى, 1444

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.