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arXiv:quant-ph/0406149

A new perturbation method in quantum mechanics

Francisco Marcelo Fernández

Published Jun 21, 2004• 0 citations
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Abstract

We investigate the convergence properties of a perturbation method proposed some time ago and reveal some of it most interesting features. Anharmonic oscillators in the strong--coupling limit prove to be appropriate illustrative examples and benchmark.
DOI
10.48550/arxiv.quant-ph/0406149

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The coupled-cluster method (CCM) of quantum many-body theory has been widely and very successfully applied to a broad spectrum of condensed-matter systems. At a given level of approximation in a hierarchy of truncations which are necessary to implement the method in practice, the many-body Schr\"odinger equation is decomposed into a finite set of coupled nonlinear equations for the various amplitudes that otherwise exactly describe the correlated clusters or subsystems within the interacting many-body medium. The properties of the multiple solutions to these equations and their implications for the method itself are the primary concern here. We perform a detailed investigation for the simple but illustrative one-body problem of a quartic anharmonic oscillator, which provides a very stringent test of the convergence properties of any method rooted in perturbation theory. The problem is treated as a model field theory in 0+1 dimensions in order to illuminate general properties of the CCM. The various supercoherent states generated by the CCM at other than the lowest levels of truncation are unnormalizable but yield finite and well-defined estimates for quantities of physical interest. Their possible use as multiphoton generalizations of the two-photon squeezed coherent states is pointed out.