Improving the accuracy of Weyl-Heisenberg wavelet and symmetrized Gaussian representations using customized phase-space-region operators

Richard Lombardini, Bill Poirier

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

A particular basis set method developed by one of the authors, involving maximally localized orthogonal Weyl-Heisenberg wavelets (or "weylets") and a phase space truncation scheme, has been successfully applied to exact quantum calculations for many degrees of freedom (DOF's). However, limitations in accuracy arise in the many-DOF case, owing to memory limits on conventional computers. This paper addresses this accuracy limitation by introducing phase space region operators (PSRO's) that customize individual weylet basis functions for the problem of interest. The construction of the PSRO's is straightforward, and does not require a priori knowledge of the desired eigenstates. The PSRO, when applied to weylets, as well as to simple phase space Gaussian basis functions, exhibits remarkable improvements in accuracy, reducing computed eigenvalue errors by orders of magnitude. The method is applied to various model systems at varying DOF's.

Original languageEnglish
Article number036705
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number3
DOIs
StatePublished - 2006

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