On the deterministic computation of functional integrals in application to quantum mechanical problems

摘要

New approximate formulae for functional integrals with Gaussian measure in separable Frechét spaces are derived. As a special case, the integration with respect to the conditional Wiener measure is investigated. For conditional Wiener integrals a family of approximate formulae with weight is constructed. The quantum mechanical models, namely the linear and the inharmonic oscillators, are described. The efficiency of the formulas is demonstrated in the numerical comparison with the Monte Carlo method on lattice.