The influence of the chameleon field potential on transition frequencies of gravitationally bound quantum states of ultra-cold neutrons

Understand

We calculate the chameleon field potential for ultracold neutrons, bouncing on top of one or between two neutron mirrors in the gravitational field of the Earth.

• For the resulting non--linear equations of motion we give approximate analytical solutions and compare them with exact numerical ones for which we propose the analytical fit.
• The obtained solutions may be used for the quantitative analysis of contributions of a chameleon field to the transition frequencies of quantum states of ultra-cold neutrons bound in the gravitational field of the Earth.