Abstract
In this paper the quantum white noise (QWN)-Euler operator Delta(Q)(E) is defined as the sum Delta(Q)(G) + N-Q, where Delta(Q)(G) and N-Q stand for appropriate QWN counterparts of the Gross Laplacian and the conservation operator, respectively. It is shown that Delta(Q)(E) has an integral representation in terms of the QWN-derivatives {D-t(-), D-t(+); t is an element of R} as a kind of functional integral acting on nuclear algebra of white noise operators. The solution of the Cauchy problem associated to the QWN-Euler operator is worked out in the basis of the QWN coordinate system.