The complex scaled Feynman–Kac formula for singular initial distributions

Abstract

In this paper we study complex scaling in the Feynman–Kac formula, using the fact that for a Dirac delta initial distribution, complex scaling is well defined in white noise analysis.

Keywords:

• white noise analysis
• Feynman–Kac formula
• Schrödinger equation
• complex scaling

2000 Mathematics Subject Classification::

• 60H40
• 81S40
• 81Q05

Acknowledgement

Financial support of Project PTDC/MAT/67965/2006 and FCT, POCTI- 219, FEDER is gratefully acknowledged.

Notes

^1. Email: [email protected].

^2. Email: [email protected]; [email protected].