In the present paper we discuss a possibility to construct both a probabilistic representation and a probabilistic approximation of the Cauchy problem solution for an equation partial derivative u/partial derivative t=sigma(2)/2 Delta u+V(x)u, where sigma is a complex parameter such that Re sigma(2) >= 0. This equation coincides with the heat equation when Im sigma(2) = 0 and with the Schrodinger equation when sigma(2) = iS where S is a positive number. (C) 2015 Elsevier B.V. All rights reserved.