Quantum Mechanical Propagators in Terms of Hida Distributions

TL;DR

This paper reviews White Noise Analysis to construct Feynman integrals as generalized functionals, demonstrating their role in solving the Schrödinger equation for various potentials.

Contribution

It introduces a novel approach to representing Feynman integrals using Hida distributions within White Noise Analysis, linking them directly to quantum dynamics.

Findings

Feynman integrals constructed as Hida distributions solve the Schrödinger equation.

The approach applies to a broad class of quantum potentials.

Provides a rigorous mathematical framework for Feynman path integrals.

Abstract

We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. After sketching this construction for a large class of potentials we show that the resulting Feynman integrals solve the Schroedinger equation.