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This article is cited in 5 scientific papers (total in 5 papers)
Functional Integrals for the Schrodinger Equation on Compact Riemannian Manifolds
Ya. A. Butko M. V. Lomonosov Moscow State University
Abstract:
In this paper, we represent the solution of the Cauchy problem for the Schrodinger equation on compact Riemannian manifolds in terms of functional integrals with respect to the Wiener measure corresponding to the Brownian motion in a manifold and with respect to the Smolyanov surface measures constructed from the Wiener measure on trajectories in the underlying space. The representation of the solution is obtained for the case of analytic (on some sets) potential and analytic initial condition under certain assumptions on the geometric characteristics of the manifold. In the proof, we use a method due to Doss and the representations via functional integrals of the solution to the Cauchy problem for the heat equation in a compact Riemannian manifold.
Received: 25.10.2004 Revised: 17.10.2005
Citation:
Ya. A. Butko, “Functional Integrals for the Schrodinger Equation on Compact Riemannian Manifolds”, Mat. Zametki, 79:2 (2006), 194–200; Math. Notes, 79:2 (2006), 178–184
Linking options:
https://www.mathnet.ru/eng/mzm2690https://doi.org/10.4213/mzm2690 https://www.mathnet.ru/eng/mzm/v79/i2/p194
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Abstract page: | 648 | Full-text PDF : | 246 | References: | 49 | First page: | 1 |
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