Extension of the correspondence principle in relativistic quantum mechanics

19 Jan 2020  ·  Hernández K. G., Aguilar S. E., Bernal J. ·

In this paper we apply the Bohr's correspondence principle to analize the asymptotic behavior of the Klein-Gordon and Dirac probability densities. It is found that in the non-relativistic limit, the densities reduce to their respective classical single-particle probability distributions plus a series of quantum corrections. The procedure is applied in two basic problems, the relativistic quantum oscillator and the relativistic particle in a box. The particle and antiparticle solutions are found to yield the same classical distribution plus quantum correction terms for the proposed limit. In the quantum oscillator case, a $\kappa$ parameter modifies the probability distribution. Its origin is briefly discussed in terms of energy.

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Quantum Physics