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