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Revista Mexicana de Física E

Solution of the Schrödinger equation for a particle in a uniform force field via the solution for a free particle

G. F. Torres del Castillo, A. S. De la Paz Cota

Published Jan 1, 2026• 0 citations
Publisher

Abstract

We show that the solutions of the Schrödinger equation for a free particle are related in a simple manner with the solutions of the Schrödinger equation for a particle in a uniform force field. Making use of this relation we readily obtain the so-called Airy wave packets and the propagator for a particle in a uniform force field.
DOI
10.31349/revmexfise.23.010215

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We present a simple approach for finding the general solution of the time-dependent Schrödinger equation for a particle moving under the action of a uniform force. From such a general solution we derive the eigenfunctions of the energy as well as those of the momentum. Next we obtain the propagator and show that the time evolution of an arbitrarily chosen initial wavefunction is described by a Fresnel transformation. This establishes a useful link with optical phenomena and allows us to link the case of a particle moving under a uniform force to that of the free particle.
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