Simpson's rule of discretized Feynman path integration (Q1182662)

The power of modern computers has penetrated most of the levels of theoretical as also numerical research work. Here the author suggests a Simpson's rule for a discretized Feynman path integral approximation of the density matrix element. For an \(N\)-step discretized representation with respect to a class of bounded-below potential functions the error bound \(O(1/N^ 2)\) is established rigorously. As a model case study, the harmonic oscillator is used to compare the new Simpson's rule with the usual trapezoidal rule indicating the superiority of the author's fresh approach.