Derivation of the harmonic oscillator propagator using the Feynman path integral and recursive relations

We present the simplest and most straightforward derivation of the one-dimensional harmonic oscillator propagator, using the Feynman path integral and recursive relations. Our calculations have pedagogical benefits for those undergraduate students beginning to learn the path integral in quantum mechanics, in that they can follow its calculations very simply with only elementary mathematical manipulation. Further, our calculations do not require cumbersome matrix algebra. (paper)