Estimate of the difference between the Kac operator and the Schrodinger semigroup

An operator norm estimate of the difference between the Kac operator and the Schrodinger semigroup is proved and used to give a variant of the Trotter product formula for Schrodinger operators in the L-p operator norm. This extends Helffer's result in the L-2 operator norm to the case in the L-p operator norm for more general scalar potentials and with vector potentials. The method of the proof is probabilistic based on the Feynman-Kac and Feynman-Kac-Ito formula.