Einstein's Equivalence Principle in Nonrelativistic Quantum Mechanics

Abstract: In this work, a precise quantum formulation of Einstein's Equivalence Principle (EEP) is developed within the framework of nonrelativistic quantum mechanics. By employing detailed analyses in both the Schr\"odinger and Heisenberg pictures, it is demonstrated that an observer in free fall in a uniform gravitational field is equivalent to an inertial observer in the absence of such a field. The transformations of the wave function are reexamined, and the conditions for the equality of inertial and gravitational mass are established -- thereby consistently deriving the gravitational redshift observed in neutron interferometry experiments. Additionally, relevant applications of the proposed formalism are explored in confined systems (such as particles in potential boxes and in linear potential barriers), elucidating quantum tunneling phenomena and their dependence on energy levels. The results reaffirm the validity of the Equivalence Principle in the nonrelativistic quantum regime and open new perspectives for integrating quantum mechanics and general relativity.