Abstract
We construct a pointwise solution for the time dependent Schrödinger equation on Rd with potentials and initial conditions which can grow exponentially at infinity and belong to the class of smooth Laplace transforms of complex measures on ℝd. The methods used are both analytic and probabilistic and the result can be looked upon as an extension of rigorously defined Feynman path integrals to the case of potentials which can strongly grow at infinity. An appendix with the calculation of some Wiener integrals is also presented.
| Original language | English |
|---|---|
| Pages (from-to) | 65-82 |
| Number of pages | 18 |
| Journal | Potential Analysis |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1998 |
Bibliographical note
Funding Information:The financial support of DFG (Z.B), SFB 237 (Z.B and Z.H), BiBoS and the EC Foundation (Z.H) is gratefully acknowledged.
Funding Information:
SFB 237 (Essen–Bochum–Dusseldorf); BiBoS; CERFIM (Locarno). Supported by DFG, current address: Department of Pure Mathematics, The University of Hull, Hull HU6 7RX, UK.
Keywords
- Feynman-Kac formula
- Laplace transform
- Schrödinger equation
ASJC Scopus subject areas
- Analysis
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