Duryagin

Class of parabolic second order equations, produced by different quantization types of one classical system’s quadratic Hamiltonian, was considered. Solution of Cauchy-Dirichlet problem for considered class of equations on the interval was represented as Hamiltonian Feynman’s formula, that is as a limit of finite-multiplicity elementary integrals when multiplicity approached infinity. New formula for direct computation of the solution to formulated problem and computer simulation of corresponding dynamics was obtained in this work. Connection between differential operators corresponding to different quantization types of quadratic Hamiltonian and connection of obtained Hamiltonian Feynman’s formula with Feynman’s path integrals in phase space were also discussed in the article.