Issue
EPL
Volume 87, Number 4, August 2009
Article Number 40006
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/87/40006
Published online 15 September 2009
EPL, 87 (2009) 40006
DOI: 10.1209/0295-5075/87/40006

Quantum mechanics and geodesic deviation in the brane world

S. M. M. Rasouli, A. F. Bahrehbakhsh, S. Jalalzadeh and M. Farhoudi

Department of Physics, Shahid Beheshti University - G. C., Evin, Tehran 19839, Iran

m-rasouli@sbu.ac.ir
af-bahrehbakhsh@sbu.ac.ir
s-jalalzadeh@sbu.ac.ir
m-farhoudi@sbu.ac.ir

received 23 May 2009; accepted in final form 13 August 2009; published August 2009
published online 15 September 2009

Abstract
We investigate the induced geodesic deviation equations in the brane world models, in which all the matter forces except gravity are confined on the 3-brane. Also, the Newtonian limit of induced geodesic deviation equation is studied. We show that in the first Randall-Sundrum model the Bohr$\hbox{--} $Sommerfeld quantization rule is as a result of consistency between the geodesic and geodesic deviation equations. This indicates that the path of test particle is made up of integral multiples of a fundamental Compton-type unit of length h/mc.

PACS
04.50.-h - Higher-dimensional gravity and other theories of gravity.
03.65.Ta - Foundations of quantum mechanics; measurement theory.
04.20.Cv - Fundamental problems and general formalism.

© EPLA 2009