TY - JOUR
T1 - Relativistic quantum bouncing particles in a homogeneous gravitational field
AU - Rohim, Ar
AU - Ueda, Kazushige
AU - Yamamoto, Kazuhiro
AU - Lin, Shih Yuin
N1 - Funding Information:
We thank Y. Kojima, Y. Kamiya, J. Murata, T. Yoshioka, T. Wakasa, J. Soda, Y. Nambu, S. Kanno, N. Matsumoto, K. Ishikawa, M. Okawa, R. B. Mann, A. S. Adam, T.-H. Li, and B. L. Hu for useful discussions and comments. This work was supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT)/Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Nos. 15H05895 and 17K05444 (KY)/Sasakawa Scientific Research Grant from the Japan Science Society/JSPS KAKENHI Grant No. 20J22946 (KU). AR is supported by Japanese Government (Monbukagakusho: MEXT) Scholarship. SYL is supported by the Ministry of Science and Technology of Taiwan under Grant No. MOST 109-2112-M-018-002 and in part by the National Center for Theoretical Sciences, Taiwan.
Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/10/1
Y1 - 2021/10/1
N2 - 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.
AB - 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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U2 - 10.1142/S021827182150098X
DO - 10.1142/S021827182150098X
M3 - Article
AN - SCOPUS:85116766412
VL - 30
JO - International Journal of Modern Physics D
JF - International Journal of Modern Physics D
SN - 0218-2718
IS - 13
M1 - 2150098
ER -