2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94200Schroedinger's equation with scalar and vector potentials is shown to describe "nothing but" hopping of a quantum particle on a lattice; any spatial variation of the hopping amplitudes acts like an external electric and/or magnetic field. The main point of the argument is the superposition principle for state vectors; Lagrangians, path integrals, or classical Hamiltonians are not (!) required. Analogously, the Hamiltonian of the free electromagnetic field is obtained as a twofold continuum limit of unitary hopping in Z(N) link configuration space, if gauge invariance and C and P symmetries are imposed.LaTeX2e, 12 pages, no figuresQuantum Physicstext