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A Coupled Cluster Technique With Iterative Bogoliubov Transformations For Computing Eigenvalues Of Perturbed Quantum Harmonic Oscillators
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2020
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The 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.
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27671289.pdf
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Physics and Astronomy