2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57268The present letter obtains the exact solution and geometric phase of the time-dependent Schrödinger equation governing the dipole oscillator in the exterior electric field, by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation. It is shown that the geometric phase presents the global property of the time evolution of the dipole oscillator in time-dependent environments.5 pages, LatexMathematical Physicstext