An Equation of Motion Coupled Cluster Approach Applied to a Set of Perturbed Quantum Mechanical Harmonic Oscillators

Abstract

We consider an Equation of Motion Coupled Cluster (EOM-CC) approach to the solution of the problem of a set of perturbed harmonic oscillators described by the normal ordered Hamiltonian [ HN =sumlimits_r=1^N hbar omega r a_r^ as +sumlimits_rs=1^N A_rs ar as +sumlimits_rs=1^N A_rs a_r^dag a_s^dag +sumlimits_rs=1^N D_rs a_r^dag as ] The EOM-CC equations are derived using diagrammatic techniques and the resulting equations are solved numerically for a number of illustrative examples. We show that the exact perturbed ground state energy is obtained with a cluster operator containing only double excitations and that the entire spectrum of the perturbed system can be generated from the knowledge of the single excitation sub-block of the transformed Hamiltonian, exp (-T2 )Hexp (T2 ).