2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159694In 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.ProbabilityFunctional Analysis60H40, 60H15, 46F25, 46G20, 81S25text