2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155999The relativistic corrections in the Hamiltonian for a particle in a uniformly rotating frame are discussed. They are shown to be negligible in the case of ultra-cold neutrons (UCN) in the Earth's gravity. The effect, on the energy levels of UCN, of the main term due to the Earth's rotation, i.e. the angular-momentum term, is calculated. The energy shift is found proportional to the energy level itself.12 pages in standard LaTeX. v3: Former sect. 2 (derivation of the non-relativistic Hamiltonian) suppressed, new refs., interpretation of the energy shift added, and new redactional improvements, to meet the editorial demands. To appear in Physics Letters AQuantum PhysicsGeneral Relativity and Quantum Cosmologytext