2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111749The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian quantum theory is obtained. The conditional transition probability density of the presence of a Browmian particle is obtained with the help of the functional integral. The technique of factorisation of the solution of the Fokker-Planck equation is employed to evaluate the effective potential energy.13 pages, no figureExactly Solvable and Integrable Systemstext