An approach to establish a connection between algebraic and configuration spaces: su(ν + 1) algebraic model for vibrational excitations

Abstract

A realisation of coordinates and momenta in the algebraic space to describe vibrational excitations of ν-equivalent oscillators is obtained. The connection between algebraic and configuration spaces is carried out using the approach recently proposed [Mol. Phys. (2017), doi:10.1080/00268976.2017.1358829]. The realisation consists in an expansion in terms of the dynamical algebra generators with coefficients determined through a minimisation procedure and given in terms of matrix elements defined in configuration space. Two realisations are presented: one through an isomorphism with a harmonic oscillators basis and the second one using a mapping to Morse oscillators. In the case of the harmonic oscillator mapping, two chains associated with coordinate and momentum representation have been identified. Our approach allows us to establish the algebraic representation of any interaction and, consequently, of the Hamiltonian associated with ν-interacting oscillators, providing a formal approach to estimate the potential energy surface.