# Accession Number:

## AD0651428

# Title:

## A HILBERT SPACE DERIVATION OF THE CLASSICAL GENERALIZED MASTER EQUATION,

# Descriptive Note:

# Corporate Author:

## NAVAL RADIOLOGICAL DEFENSE LAB SAN FRANCISCO CALIF

# Personal Author(s):

# Report Date:

## 1967-03-29

# Pagination or Media Count:

## 38.0

# Abstract:

The ket-vector notation of Dirac is used to formulate the classical Liouville equation in a Hilbert space of functions spanned by the eigenkets of the Liouville operator. The formalism applies to finite as well as infinte systems. The solutions of the inhomogeneous Liouville equation is considered where the inhomogeneity is taken as the perturbation. The Hilbert space formalism allows the introduction of projection operators, and the derivation of the generalized master equations without perturbation theory. In the weak coupling limit this is shown to reduce to the Brout-Prigogine equation. A thermodynamic interpretation is given to spacially inhomogeneous terms in the equation. Author

# Subject Categories:

- Physical Chemistry
- Theoretical Mathematics