%0 Journal Article
%T Quantum Gross Laplacian and Applications
%A Habib Ouerdiane
%A Samah Horrigue
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0804.3938v1