Abstract.
In this article we have investigated theoretical aspects of the solutions of some of the quantum mechanical problems in Rindler space. We have developed formalisms for the exact analytical solutions for the relativistic equations, along with the approximate form of solutions for the Schrödinger equation. The Hamiltonian operator in Rindler space is found to be non-Hermitian in nature, whereas the energy eigen values are observed to be real in nature. We have noticed that the sole reason behind such real behavior is the PT -symmetric form of the Hamiltonian operator. We have also observed that the energy eigen values are negative, lineraly quantized and the quantum mechanical system becomes more and more bound with the increase in the strength of gravitational field strength produced by the strongly gravitating objects, e.g., black holes, which is classical in nature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields (Butterworth-Heimenann, Oxford, 1975)
N.D. Birrell, P.C.W. Davies, Quantum Field Theory in Curved Space (Cambridge University Press, Cambridge, 1982)
C.W. Misner, Kip S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman and Company New York, 1972)
W. Rindler, Essential Relativity (Springer-Verlag, New York, 1977)
G.F. Torres del Castillo, C.L. Perez Sanchez, Rev. Mex. Fis. 52, 70 (2006)
Domingo J. Louis-Martinez, Class. Quantum Grav. 28, 035004 (2011) arXiv:1012.3063
M. Socolovsky, Ann. Found. Louis de Broglie 39, 1 (2014)
C.-G. Huang, J.-R. Sun, Commun. Theor. Phys. 49, 928 (2008) arXiv:gr-qc/0701078
Nicola Vona, Master Thesis in Physics, Universitá di Napoli Federico II (2007)
Carl M. Bender, arXiv:quant-ph/0501052 (and references therein)
Sanchari De, Sutapa Ghosh, Somenath Chakrabarty, Mod. Phys. Lett. A 30, 1550182 (2015)
Sanchari De, Sutapa Ghosh, Somenath Chakrabarty, Astrophys. Space Sci. 360, 8 (2015)
R.H. Fowler, Dr.L. Nordheim, Proc. R. Soc. London 119, 173 (1928)
A. Ghosh, S. Chakrabarty, Mon. Not. R. Astron. Soc. 425, 1239 (2012) and references therein
M. Abramowitz, I.A. Stegun (Editors), Handbook of Mathematical Functions (Dovar Publications Inc., 1970)
F. Brau, arXiv:hep-ph/9903209
P. Cea, G. Nardulli, G. Paiano, Phys. Rev. D 28, 2291 (1983)
S.N. Gupta, S.F. Radford, W.W. Repko, Phys. Rev. D 31, 160 (1985)
G. Boole, Phil. Trans. R. Soc. London 134, 225 (1844)
A.A. Matyshev, E. Fohtung, arXiv:0910.0365 [math-ph]
L.S. Gradshteyn, I.M. Ryzhik, Table of Integrals (Academic Press, Inc., New York, 1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mitra, S., Chakrabarty, S. Some theoretical aspects of quantum mechanical equations in Rindler space. Eur. Phys. J. Plus 132, 114 (2017). https://doi.org/10.1140/epjp/i2017-11392-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11392-1