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arXiv · 1907.05842

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

K. G. Hernández·S. E. Aguilar·J. Bernal
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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.

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K. G. Hernández, S. E. Aguilar, J. Bernal. 2019-07-12. On the correspondence principle for the Klein-Gordon and Dirac Equations. https://doi.org/10.30495/jtap.162244

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