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arXiv · 2005.13264

Relativistic quantum bouncing particles in a homogeneous gravitational field

Ar Rohim·Kazushige Ueda·Kazuhiro Yamamoto·Shih-Yuin Lin
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Abstract

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein-Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein-Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

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Ar Rohim, Kazushige Ueda, Kazuhiro Yamamoto, Shih-Yuin Lin. 2022-03-22. Relativistic quantum bouncing particles in a homogeneous gravitational field. https://doi.org/10.1142/s021827182150098x

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