Quantum effects in a one-dimensional magnetic gravitational trap for ultracold neutrons

The problem of storing ultracold neutrons over a plane magnetic mirror in the presence of gravity is considered. For neutrons with a definite polarization, the sum of the magnetic and gravitational potentials can have a minimum and, hence, form a magnetic gravitational trap. For low energies of vertical motion, the neutron state in this well is quantized. The possibility of accomplishing the corresponding quantum gravitational experiment is analyzed.