Quantization of neutron in Earth's gravity

TL;DR

This paper analyzes the quantum states of neutrons in Earth's gravity, showing that observed energy levels are due to confinement potential rather than gravitational effects, and highlights the challenge of detecting such shallow states.

Contribution

It clarifies that the observed neutron energy levels are caused by experimental confinement, not Earth's gravity, and provides a theoretical estimate of the true gravitational quantum states.

Findings

Observed energy levels are 10^{25} times deeper than gravitational levels.

The actual gravitational energy of a neutron's ground state is around 10^{-37} eV.

Experimental results are due to confinement potential, not gravity.

Abstract

Gravity is the weakest of all four known forces in the universe. Quantum states of an elementary particle due to such a weak field is certainly very shallow and would therefore be an experimental challenge to detect. Recently an experimental attempt was made by V. V. Nesvizhevsky et al., Nature 415, 297 (2002), to measure the quantum states of a neutron, which shows that ground state and few excited states are \sim 10^{-12}eV. We show that the energy of the ground state of a neutron confined above Earth's surface should be \sim 10^{-37}eV. The experimentally observed energy levels are 10^{25} times deeper than the actual energy levels it should be and thus certainly not due to gravitational effect of Earth. Therefore the correct interpretation for the painstaking experimental results of Ref. \cite{nes1} is due to the confinement potential of a one dimensional box of length L \sim 50\mu m, generated from the experimental setup as commented before \cite{hansoon}. Our results thus creates a new challenge to the experimentalist to resolve the shallow energy levels of the neutron in Earth's gravitational field in future.