Quantum Gross Laplacian and Applications
Probability
2008-04-25 v1 Functional Analysis
Abstract
In this paper, we introduce and study a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian. Then, applying the quantum Gross Laplacian to the particular case where the operator is the multiplication operator, we find a relation between classical and quantum Gross Laplacian. As application, we give explicit solution of linear quantum white noise differential equation. In particular, we give a explicit solution of the quantum Gross heat equation.
Cite
@article{arxiv.0804.3938,
title = {Quantum Gross Laplacian and Applications},
author = {Habib Ouerdiane and Samah Horrigue},
journal= {arXiv preprint arXiv:0804.3938},
year = {2008}
}