used in this context. As far as we know, this method was used for the first time in non-relativistic quantum mechanics by Urrutia and Hernandez [@UrrutiaHernandez1984]. These authors used Schwinger’s action principle to obtain the Feynman propagator for a damped harmonic oscillator with a time-dependent frequency under a time-dependent external force. Up to our knowledge, since then only a few papers have been written with this method, namely: in 1986, Urrutia and Manterola [@UrrutiaManterola1986] used it in the problem of an anharmonic charged oscillator under a magnetic field; in the same year, Horing, Cui, and Fiorenza [@HoringCuiFiorenza1986] applied Schwinger’s method to obtain the Green function for crossed time-dependent electric and magnetic fields; the method was later applied in a rederivation of the Feynman propagator for a harmonic oscillator with a time-dependent frequency [@FarinaSegui1993]; a connection with the mid-point-rule for path integrals involving electromagnetic interactions was discussed in [@RabelloFarina1995]. Finally, pedagogical presentations of this method can be found in the recent publication [@BaroneBoschiFarinaAJP2003] as well as in Schwinger’s original lecture notes recently published [@SchwingerBookEnglert2001], which includes a discussion of the quantum action principle and a derivation of the method to calculate propagators with some examples.

It is worth mentioning that this 