2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108030For a prescribed pair of quantum states |psi_I> and |psi_F> we establish an elementary derivation of the optimum Hamiltonian, under constraints on its eigenvalues, that generates the unitary transformation |psi_I> --> |psi_F> in the shortest duration. The derivation is geometric in character and does not rely on variational calculus.5 pagesQuantum Physicstext