A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations
Vassili Nikitich Kolokoltsov
Solutions to the Schrödinger, heat and stochastic Schrödinger equation with rather general potentials are represented, both in x- and p-representations, as integrals over the path space with respect to σ-finite measures. In the case of x-representation, the corresponding measure is concentrated on the Cameron–Martin Hilbert space of curves with L2-integrable derivatives. The case of the Schrödinger equation is treated by means of a regularization based on the introduction of either complex times or continuous non-demolition observations.
Mathematical Proceedings of the Cambridge Philosophical Society•Mar 1, 2002•12 citations