ALGEBRAIC TREATMENT OF A 3-OSCILLATOR SYSTEM - APPLICATIONS TO SOME MOLECULAR-MODELS

A new algebraic treatment of a three-oscillator system, called 3d form alism, is proposed. First, arbitrary tensor operators, expressed in te rms of elementary creation and annihilation boson operators, are built within the standard algebraic chain u(3) <superset of so(3) superset of so(2). Their matrix elements are next derived in a standard basis. Some applications, which require few adaptions or extensions, are prop osed. They allow one Lo recover, for instance, Hecht's and tetrahedral Hamiltonians associated with threefold degenerate modes of spherical molecules and the vibron model Hamiltonian introduced for diatomic mol ecules. (C) 1997 Academic Press.