White Noise Functional Integrals in Quantum Mechanics

Nobuaki Obata

Ludwig Streit

Diego de Falco, Dinkar C. Khandekar

Aymen Ettaieb, Habib Ouerdiane, Hafedh M. S. Rguigui

In this paper we give the integral representation of the power of the quantum white noise (QWN) Euler operator (∆ Q E ) ρ , for ρ ∈ N, in terms of the QWN-derivatives {D - t , D + t ; t ∈ R} as a kind of functional integral acting on nuclear algebra of white noise operators.The solution of the Cauchy problem associated to (∆ Q E ) ρ is worked out in the basis of the QWN coordinate system.

Viktor Nikolayevich Popov

Abdessatar Barhoumi, Habib Ouerdiane, Hafedh M. S. Rguigui

In this paper the quantum white noise (QWN)-Euler operator [Formula: see text] is defined as the sum [Formula: see text], where [Formula: see text] and NQ stand for appropriate QWN counterparts of the Gross Laplacian and the conservation operator, respectively. It is shown that [Formula: see text] has an integral representation in terms of the QWN-derivatives [Formula: see text] 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.