Notes on the Feynman integral. III. The Schroedinger equation

Gerald William Johnson and David Lee Skoug

Vol. 105 (1983), No. 2, 321–358

DOI: 10.2140/pjm.1983.105.321

Abstract

In the setting of Cameron and Storvick’s recent theory we show that the solution of an integral equation formally equivalent to the Schroedinger equation is expressible as the analytic Feynman integral of a function on ν-dimensional Wiener space of the form F(X) = exp{∫ ₀^t𝜃(t − s,X(s) + ξ)ds}ψ(X(t) + ξ). Here X is an R^ν-valued continuous function on [0,t] such that X(0) = 0, ξ ∈ R^ν, and ψ and 𝜃(s,⋅) are Fourier-Stieltjes transforms.

Mathematical Subject Classification 2000

Primary: 81C35, 81C35

Secondary: 28B05, 46G99, 58D30

Milestones

Received: 10 June 1981

Revised: 26 August 1981

Published: 1 April 1983