On the Trotter formula computation of the kernel for the harmonic oscillator (Q1820264)

Feynman and Hibbs' original method of computing the path integral representing the kernel of exp(itH), where H is the harmonic oscillator Hamiltonian, by expanding the path in Fourier series and integrating over the coefficients of the latter, is shown to give the wrong answer. The author presents a derivation starting from Trotter's formula on which the origin of the mistake can be traced to replacing \(\cos (\pi j/n)\) by \(1- (\pi j/n)^ 2\) in a product over \(j=1,...,n-1\) \((n\to \infty).\)