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    The Feynman-Kac-Ito formula for an infinite-dimensional Schrodinger equation with a scalar and vector potential

    2006, Vol. 2, No. 1, pp.  75-87

    Author(s): Butko Y. A.

    We consider an infinite-dimensional Schrodinger equation with a scalar and vector potential 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 that mimics the Feynman-Kac-Ito formula.
    Keywords: infinite dimensional Schrodinger equation, stochastic integrals, vector potential, Feynman-Kac-Ito formula, functional integrals
    Citation: Butko Y. A., The Feynman-Kac-Ito formula for an infinite-dimensional Schrodinger equation with a scalar and vector potential, Rus. J. Nonlin. Dyn., 2006, Vol. 2, No. 1, pp.  75-87
    DOI:10.20537/nd0601004


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