https://doi.org/10.1140/epjc/s10052-013-2609-1
Regular Article - Theoretical Physics
Exact ultra cold neutrons’ energy spectrum in gravitational quantum mechanics
Department of Physics, Science and Research Branch, Islamic Azad University, Tehran, Iran
* e-mail: p.pedram@srbiau.ac.ir
Received:
23
May
2013
Revised:
24
September
2013
Published online:
18
October
2013
We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to 
and a maximal momentum proportional to 
, where β is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spectrometers. Then, based on Nesvizhevsky’s famous experiment, we obtain an upper bound on the dimensionless GUP parameter.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013
