Rittby, C. Magnus L.2020-01-032020-01-0320202020https://repository.tcu.edu/handle/116099117/36207The details of a coupled cluster technique making use of iterative Bogoliubov transformations for the calculation of the ground and excited states of a coupled set of perturbed harmonic oscillators are developed. A diagrammatic approach is presented and implemented for the efficient development of cluster amplitude and energy equations. The method is applied to a quadratic and quartic perturbations to illustrate the power of Bogoliubov transformations in providing an improved zeroth order Hamiltonian for perturbative methods. Some initial numerical results for a single quartic oscillator are also presented showing good agreement with exact results obtained from numerical integration of the Schrdinger equation. A new iterative Bogoliubov transformation scheme is applied and shown to improve the agreement with exact results considerably. Finally, explicit coupled cluster and energy equations are presented for a set of coupled oscillators subjected to cubic and quartic perturbations.Format: OnlineNo search engine accessText