A remark concerning Feynman Kac formulas for the perturbed harmonic oscillator

TL;DR

This paper provides explicit Wiener space integral solutions for parabolic evolution problems involving time-dependent perturbations of the harmonic oscillator's heat equation.

Contribution

It introduces a novel approach to solving perturbed harmonic oscillator heat equations using Wiener space integrals.

Findings

Explicit Wiener space integral representations derived.

Applicable to time-dependent perturbations of the harmonic oscillator.

Enhances understanding of stochastic representations in quantum mechanics.

Abstract

We give the solution of certain parabolic evolution problems (time-depending perturbations of the heat equation for the harmonic oscillator) as explicit integrals on the Wiener space.