Test of the Equivalence Principle for Neutrons in Earth's Gravitational Field

The paper proposes a method for high-precision testing of the equivalence principle for neutrons by calculating their weakly bound quantum states in the weak gravitational field of the Earth. Using the nonrelativistic Schrödinger equation, the energy spectrum of a neutron was obtained taking into account a possible violation of the equality between its gravitational and inertial masses. It is shown that, with a relative violation of the equivalence principle at the level of current experimental constraints 10 −4 , the relative shift of highly excited quantum levels can reach an order of 10 −3 . This method demonstrates the potential of precision spectroscopy of neutron quantum states for testing the equivalence principle and searching for manifestations of quantum gravity.