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Russian Journal of Mathematical Physics

Schrödinger Equation with Signed Hamiltonian

А. А. Лобода

Published Jan 1, 2020• 1 citation
Publisher

Abstract

A functional integral with respect to the Wiener measure that represents a solution of the Schrödinger equation with signed Hamiltonian is obtained. In turn, this integral is derived, using the analytic continuation with respect to the argument, from a similar integral for the corresponding heat equation.
DOI
10.1134/s1061920820010094

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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.
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