Monte Carlo integration of the Feynman propagator in imaginary time

Abstract The Feynman propagator or “integral over paths” is written with time t replaced by −iτ. The result is a propagator, corresponding to a diffusion equation with the classical Lagrangian replaced by the classical Hamiltonian in the kernel. An evaluation of this propagator, over a sufficiently long time, yields the absolute square of the ground-state wavefunction, viz., ‖ U 0 ( χ )‖ 2 of the quantum system. A biased Monte Carlo integration scheme, where the biasing is exponential in the energy of the system, is used to evaluate functional integrals in the case of the quantum mechanical particle in a box, oscillator, and Morse potential. This scheme and the results of the integrations are described.

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