Feynman integrals for a class of exponentially growing potentials

TL;DR

This paper develops a method to construct Feynman integrals for certain exponentially growing potentials in quantum mechanics, demonstrating they satisfy the Schrödinger equation, with the Morse potential as a specific example.

Contribution

It introduces a novel approach to define Feynman integrals for exponentially growing potentials using white noise functionals, extending the mathematical framework of quantum mechanics.

Findings

Feynman integrals constructed for exponential potentials

Solutions to the Schrödinger equation verified for these integrals

Application demonstrated with Morse potential as a special case

Abstract

We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schroedinger equation. The Morse potential is considered as a special case.