Abstract Recently general conditions have been given which imply the existence of the Feynman integral as a Hida distribution. Here we perform an explicit construction of these distributions for a large class of Schrödinger problems.
Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to time-dependent potentials. This involves an expectation w.r.t. a complex scaled Brownian motion. As examples polynomial potentials of degree 4n+2,n∈N, and singular potentials of the form ∣x∣n1,n∈N and xn1,n∈N, are worked out.