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A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations

Published online by Cambridge University Press:  14 March 2002

VASSILI N. KOLOKOLTSOV
VASSILI N. KOLOKOLTSOV
Affiliation:
Nottingham Trent University, Department Math. Stat. and O.R. Burton Street, Nottingham NG1 4BU. e-mail: [email protected]
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 132 , Issue 2 , March 2002 , pp. 353 - 375
Copyright
2002 Cambridge Philosophical Society

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