A fast method for solving both the time-dependent Schrödinger equation in angular coordinates and its associated " m -mixing" problem

Matthew G. Reuter; Mark A. Ratner; Tamar Seideman

doi:10.1063/1.3213436

A fast method for solving both the time-dependent Schrödinger equation in angular coordinates and its associated " m -mixing" problem

Matthew G. Reuter, Mark A. Ratner, Tamar Seideman

Northwestern University

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

An efficient split-operator technique for solving the time-dependent Schrödinger equation in an angular coordinate system is presented, where a fast spherical harmonics transform accelerates the conversions between angle and angular momentum representations. Unlike previous techniques, this method features facile inclusion of azimuthal asymmetries (solving the " m -mixing" problem), adaptive time stepping, and favorable scaling, while simultaneously avoiding the need for both kinetic and potential energy matrix elements. Several examples are presented.

Original language	English
Article number	094108
Journal	Journal of Chemical Physics
Volume	131
Issue number	9
DOIs	https://doi.org/10.1063/1.3213436
Publication status	Published - 2009

ASJC Scopus subject areas

Physics and Astronomy(all)
Physical and Theoretical Chemistry

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title = "A fast method for solving both the time-dependent Schr{\"o}dinger equation in angular coordinates and its associated {"} m -mixing{"} problem",

abstract = "An efficient split-operator technique for solving the time-dependent Schr{\"o}dinger equation in an angular coordinate system is presented, where a fast spherical harmonics transform accelerates the conversions between angle and angular momentum representations. Unlike previous techniques, this method features facile inclusion of azimuthal asymmetries (solving the {"} m -mixing{"} problem), adaptive time stepping, and favorable scaling, while simultaneously avoiding the need for both kinetic and potential energy matrix elements. Several examples are presented.",

author = "Reuter, {Matthew G.} and Ratner, {Mark A.} and Tamar Seideman",

note = "Funding Information: We are grateful to Dr. Jeff R. Hammond and Dr. Thorsten Hansen for interesting conversations and to the NSF Chemistry Division (Grant No. CHE-0616927) for their generous support. M.G.R. thanks the DoE Computational Science Graduate Fellowship Program (Grant No. DE-FG02-97ER25308) for a graduate fellowship. ",

year = "2009",

doi = "10.1063/1.3213436",

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T1 - A fast method for solving both the time-dependent Schrödinger equation in angular coordinates and its associated " m -mixing" problem

AU - Reuter, Matthew G.

AU - Ratner, Mark A.

AU - Seideman, Tamar

N1 - Funding Information: We are grateful to Dr. Jeff R. Hammond and Dr. Thorsten Hansen for interesting conversations and to the NSF Chemistry Division (Grant No. CHE-0616927) for their generous support. M.G.R. thanks the DoE Computational Science Graduate Fellowship Program (Grant No. DE-FG02-97ER25308) for a graduate fellowship.

PY - 2009

Y1 - 2009

N2 - An efficient split-operator technique for solving the time-dependent Schrödinger equation in an angular coordinate system is presented, where a fast spherical harmonics transform accelerates the conversions between angle and angular momentum representations. Unlike previous techniques, this method features facile inclusion of azimuthal asymmetries (solving the " m -mixing" problem), adaptive time stepping, and favorable scaling, while simultaneously avoiding the need for both kinetic and potential energy matrix elements. Several examples are presented.

AB - An efficient split-operator technique for solving the time-dependent Schrödinger equation in an angular coordinate system is presented, where a fast spherical harmonics transform accelerates the conversions between angle and angular momentum representations. Unlike previous techniques, this method features facile inclusion of azimuthal asymmetries (solving the " m -mixing" problem), adaptive time stepping, and favorable scaling, while simultaneously avoiding the need for both kinetic and potential energy matrix elements. Several examples are presented.

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