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.
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