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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 nonlinear 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 ultracold neutrons bound in the gravitational field of the Earth.
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Ivanov et al. (2013) studied this question.
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