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

TL;DR

This paper explores isospectral potentials related to neutron gravitational states, constructing and constraining them with experimental data, and discusses their implications for possible modifications of Newtonian gravity at very short distances.

Contribution

The study explicitly constructs isospectral potentials to the Newton potential and constrains them using neutron gravitational state data, offering insights into potential deviations from Newtonian gravity.

Findings

Constructed isospectral potentials compatible with neutron data

Wave functions and fluxes analyzed for ground and excited states

Potential deviations from Newtonian gravity at submillimetre scales are plausible

Abstract

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.