Schwinger's method and the computation of determinants

We show how to use Schwinger's method to evaluate determinants of differential operators that appear quite often in ordinary quantum mechanics. Although this method was introduced by Schwinger in the early fifties to compute effective actions for quantum electrodynamics and was recently applied by him in the Casimir effect, it has never been used in nonrelativistic problems. As explicit examples we compute the partition functions for both the bosonic and the fermionic harmonic oscillator. (C) 1998 American Association of Physics Teachers.