Interpretation of the neutron quantum gravitational states in terms of isospectral potentials

Details Interpretation of the neutron quantum gravitational states in terms of isospectral potentials Interpretation of the neutron quantum gravitational states in terms of isospectral potentials

2009-07-29

arxiv.org/abs/0907.5216v2

Physics

Nuclear Physics

Nuclear Theory

12 pages, 3 figures, 1 table. Using RevTeX4. Excited state contributions included, more extensive discussion, added references

Scientific paper

The recently observed quantum states of neutrons bound in a gravitational field are analyzed in the framework of one-parameter isospectral hamiltonians. Potentials isospectral to the usual Newton potential are explicitly constructed for the first time, then constrained using measured properties of the neutron gravitational states. The corresponding wave functions and the neutron fluxes are also calculated and analyzed in a simple model, including the ground state and the excited state contributions. The constructed isospectral potentials are discussed as candidates for a possible modification of Newton's law at a submillimetre scale. Our results indicate that significant deviations from the Newtonian gravity at submillimetre distances could be compatible with experiment.

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