arXiv subjects
Publications and source records attributed to A. Aragao.
We propose an expansion of the unitary evolution operator, associated to a given Schrödinger equation, in terms of a finite product of explicit unitary operators. In this manner, this unitary expansion can be truncated at the desired level of approximation, as shown in the given examples.
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 $\mathversion{bold}$π$ = {\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.