title: Quantum Dynamics in Phase Space using Projected von Neumann Bases.
abstract: We describe the mathematical underpinnings of the biorthogonal von Neumann method for quantum mechanical simulations (PvB). In particular, we present a detailed discussion of the important issue of nonorthogonal projection onto subspaces of biorthogonal bases, and how this differs from orthogonal projection. We present various representations of the Schrödinger equation in the reduced basis and discuss their relative merits. We conclude with illustrative examples and a discussion of the outlook and challenges ahead for the PvB representation.
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science , 76100 Rehovot, Israel.
authors.forename: Shai
authors.initials: S
authors.lastname: Machnes
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science , 76100 Rehovot, Israel.
authors.forename: Elie
authors.initials: E
authors.lastname: Assémat
authors.affiliation: Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel , Olshausenstraße 40, D-24098 Kiel, Germany.
authors.forename: Henrik R
authors.initials: HR
authors.lastname: Larsson
authors.affiliation: Department of Chemical Physics, Weizmann Institute of Science , 76100 Rehovot, Israel.
authors.forename: David J
authors.initials: DJ
authors.lastname: Tannor