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- Title
Relativistic quantum bouncing particles in a homogeneous gravitational field.
- Authors
Rohim, Ar; Ueda, Kazushige; Yamamoto, Kazuhiro; Lin, Shih-Yuin
- 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.
- Subjects
GRAVITATIONAL fields; GRAVITATIONAL potential; DIRAC equation; WAVE functions; MINKOWSKI space; SCHRODINGER equation; NONRELATIVISTIC quantum mechanics
- Publication
International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology, 2021, Vol 30, Issue 13, p1
- ISSN
0218-2718
- Publication type
Article
- DOI
10.1142/S021827182150098X