Phase‐Space Versus Coordinate‐Space Methods: Prognosis for Large Quantum Calculations

David Tannor, Shai Machnes, Elie Assemat, Henrik R. Larsson

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter provides a simple pedagogical presentation of the discrete variable representation (DVR). It reviews the von Neumann (vN) basis of phase‐space Gaussians which include the Projected von Neumann Basis (PvN) and the Biorthogonal von Neumann Basis (PvB). The chapter includes a variety of interesting formal properties of nonorthogonal bases that are an extension of the DVR presentation and provides insight into the method. It presents an analysis of multidimensional considerations, including details of a highly efficient tensor formulation for performing pruned multidimensional DVR calculations for sparse but unstructured grids. The chapter contains illustrative applications. Pruned phase‐space methods have been successfully used for computing eigenenergies of (ro‐) vibrational systems. The chapter focuses on the applications in the context of solving the time‐dependent Schrodinger equation (TDSE). The efficiency of phase‐space versus coordinate‐space methods will certainly depend on the particular system studied and the strength of coupling between degrees of freedom.
Original languageEnglish
Title of host publicationAdvances in Chemical Physics, volume 163
EditorsKB Whaley
PublisherWiley Blackwell
Pages273-323
Number of pages51
ISBN (Electronic)9781119374978
ISBN (Print)9781119374992
DOIs
StatePublished - 8 May 2018

Publication series

NameAdvances in Chemical Physics
Volume163
ISSN (Print)0065-2385

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