homogeneous gravitational field
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Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin

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.


2011 ◽  
Vol 26 (07) ◽  
pp. 481-488
Author(s):  
J. I. RIVAS ◽  
A. CAMACHO

The behavior of a Bose–Einstein condensate in a homogeneous gravitational field is analyzed. We consider two different trapping potentials. Firstly, the gas is inside a finite container. The effects of the finiteness of the height of the container in connection with the presence of a homogeneous gravitational field are mathematically analyzed and the resulting energy eigenvalues are deduced and used to obtain the corresponding partition function and ensuing thermodynamical properties. Secondly, the trapping potential is an anisotropic harmonic oscillator and the effects of the gravitational field and of the zero-point energy on the condensation temperature are also considered. These results are employed in order to put forward an experiment which could test the so-called Einstein Equivalence Principle.


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