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Exact ultra cold neutrons’ energy spectrum in gravitational quantum mechanics

  • Pouria PedramEmail author
Regular Article - Theoretical Physics

Abstract

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 \(\hbar\sqrt{\beta}\) and a maximal momentum proportional to \(1/\sqrt{\beta}\), 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.

Keywords

Quantum Gravity Generalize Uncertainty Principle Maximal Momentum Ordinary Quantum Mechanic Ultra Cold Neutron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I am very grateful to Achim Kempf for insightful comments and suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Department of Physics, Science and Research BranchIslamic Azad UniversityTehranIran

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