2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147771A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and instability of cold stars. Our procedure deriving the Hamiltonian is based on an analysis of the process of the observation with the background of the notion of quantum-mechanical local times compatible with general theory of relativity.31 pages, AmSTeXGeneral Relativity and Quantum Cosmologytext