Abstract
This paper reports on the characterization of the quantum white noise (QWN) Gross Laplacian based on nuclear algebra of white noise operators acting on spaces of entire functions with.-exponential growth of minimal type. First, we use extended techniques of rotation invariance operators, the commutation relations with respect to the QWN-derivatives and the QWN-conservation operator. Second, we employ the new concept of QWN-convolution operators. As application, we study and characterize the powers of the QWN-Gross Laplacian. As for their associated Cauchy problem it is solved using a QWN-convolution and Wick calculus.