Three Methods for Computing the Feynman Propagator
  We present three methods for calculating the Feynman propagator for the non-relativistic harmonic oscillator. The first method was employed by Schwinger a half a century ago, but has rarely been used in non-relativistic problems since. Also discussed is an algebraic method and a path integral method so that the reader can compare the advantages and disadvantages of each method. 
F. A. Barone, H. Boschi-Filho, C. Farina