Geodesic
The Feynman-Kac-Ito formula for an infinite-dimensional Schr\"odinger equation with scalar and vector potentials
Russian journal of nonlinear dynamics, Tome 2 (2006) no. 1, pp. 75-87

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We consider an infinite-dimensional Schrödinger equation with scalar and vector potentials in a Hilbert space. The vector potential plays the same role as a magnetic field in the finite-dimensional case. We have proved the existence of the solution to the Cauchy problem. The solution is local in time and space variables and is expressed by a probabilistic formula of Feynman–Kac–Ito type.
Keywords: infinite dimensional Schrödinger equation, stochastic integrals, vector potential, functional integrals.
Mots-clés : Feynman–Kac–Ito formula 
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     author = {Ya. A. Butko},
     title = {The {Feynman-Kac-Ito} formula for an infinite-dimensional {Schr\"odinger} equation with scalar and vector potentials},
     journal = {Russian journal of nonlinear dynamics},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/ND_2006_2_1_a3/}
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Ya. A. Butko. The Feynman-Kac-Ito formula for an infinite-dimensional Schr\"odinger equation with scalar and vector potentials. Russian journal of nonlinear dynamics, Tome 2 (2006) no. 1, pp. 75-87. http://geodesic.mathdoc.fr/item/ND_2006_2_1_a3/