Feynman Formula and Poisson Processes for Gentle Perturbations

Abstract

Let H = H₀ + V be a Hamiltonian, the solution of the corresponding Schrödinger equation is expected to be given by the Feynman path integral [1]

$$ \psi (X,T) = \int\limits_{\Gamma } {{e^{{ - i{S_{0}}(X,\gamma )}}} - i\int\limits_{o}^{T} {V(X - \gamma (t))dt} } \psi (X - \gamma (o))d\gamma $$

where S₀ is the free classical action associated with a path γ ∈ Γ, V is the potential and dγ is expected to be a measure.