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Feynman integrals for a class of exponentially growing potentials

Kuna, T, Ludwig Streit, Westerkamp, W

Published Jan 1, 1998• 35 citations
OpenAlex

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 Schrodinger equation. The Morse potential is considered as a special case. (C) 1998 American Institute of Physics.

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Feynman integrals for a class of exponentially growing potentials

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•Aug 17, 2016•18 citations
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,4n+2, n\in\mathbb N,4n+2,n∈N, and singular potentials of the form 1∣x∣n,n∈N\frac{1}{|x|^n}, n\in\mathbb N∣x∣n1​,n∈N and 1xn,n∈N,\frac{1}{x^n}, n\in\mathbb N,xn1​,n∈N, are worked out.