Remark on the solution of the Schrödinger equation for anharmonic oscillators via the Feynman path integral

We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t ≤ 0. As a consequence the Schrödinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space.