Feynman formulas for the Schrödinger equations with the Vladimirov operator

Abstract

A Feynman formula for heat-type equations with respect to functions defined on the product of a real line and the space ℚpn is obtained. By a Feynman formula we mean a representation of a solution of the Cauchy problem for the differential evolution equation as a limit of integrals over Cartesian powers of some space. The result thus obtained sharpens results of the paper [1]. The role of the Laplace operator is played here by the Vladimirov operator. Equations of this type turned out to be useful when describing the dynamics of proteins.