  In order to popularize the so called Schwinger's method we reconsider the
Feynman propagator of two non-relativistic systems: a charged particle in a
uniform magnetic field and a charged harmonic oscillator in a uniform magnetic
field. Instead of solving the Heisenberg equations for the position and the
canonical momentum operators, ${\bf R}$ and ${\bf P}$, we apply this method by
solving the Heisenberg equations for the gauge invariant operators ${\bf R}$
and $\mathversion{bold}${\pi}$ = {\bf P}-e{\bf A}$, the latter being the
mechanical momentum operator. In our procedure we avoid fixing the gauge from
the beginning and the result thus obtained shows explicitly the gauge
dependence of the Feynman propagator.
