2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169416We introduce the concept of interpolation in quantum evolution and present a general framework to find the energy optimal Hamiltonian for a quantum system evolving among a given set of middle states using variational and geometric methods. A few special cases are carefully studied. The quantum brachistochrone problem is proved as a special case.8 pages, 0 figuresQuantum Physicstext