Correct short time propagator for Feynman path integration by power series expansion in Δt

Nancy Makri; William H. Miller

doi:10.1016/0009-2614(88)80058-7

Correct short time propagator for Feynman path integration by power series expansion in Δt

Nancy Makri, William H. Miller

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

Abstract

The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated "improved" ones) is not correct through first order in the time increment Δt. The correct result for the phase (i.e. the action) of the short time propagator is developed in this paper as a power series in Δt, explicit expressions being given for the terms of order Δt^-1, Δt, and Δt³. Test applications to the standard harmonic oscillator and also to a double well potential (typical for intramolecular H-atom transfer) show the first-order propagator (i.e. the correct result through order Δt) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).

Original language	English (US)
Pages (from-to)	1-8
Number of pages	8
Journal	Chemical Physics Letters
Volume	151
Issue number	1-2
DOIs	https://doi.org/10.1016/0009-2614(88)80058-7
State	Published - Oct 7 1988
Externally published	Yes

ASJC Scopus subject areas

General Physics and Astronomy
Physical and Theoretical Chemistry

Online availability

10.1016/0009-2614(88)80058-7

Library availability

Discover UIUC Full Text

Cite this

@article{d610e5ef3d0e4adfaf20dc4e6784a297,

title = "Correct short time propagator for Feynman path integration by power series expansion in Δt",

abstract = "The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated {"}improved{"} ones) is not correct through first order in the time increment Δt. The correct result for the phase (i.e. the action) of the short time propagator is developed in this paper as a power series in Δt, explicit expressions being given for the terms of order Δt-1, Δt, and Δt3. Test applications to the standard harmonic oscillator and also to a double well potential (typical for intramolecular H-atom transfer) show the first-order propagator (i.e. the correct result through order Δt) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).",

author = "Nancy Makri and Miller, {William H.}",

note = "Funding Information: This work has been supportedb y the Director, Office of Energy Research,O ffice of Basic Energy Sciences, Chemical SciencesD ivision of the US Departmento f Energy under Contract No. DE-AC03-76SF00098. Support of the Berkeley Theoretical Chemistry Computational Facility by National Science Foundation Grant CHE8C16345 is gratefully acknowledged.",

year = "1988",

month = oct,

day = "7",

doi = "10.1016/0009-2614(88)80058-7",

language = "English (US)",

volume = "151",

pages = "1--8",

journal = "Chemical Physics Letters",

issn = "0009-2614",

publisher = "Elsevier B.V.",

number = "1-2",

}

TY - JOUR

T1 - Correct short time propagator for Feynman path integration by power series expansion in Δt

AU - Makri, Nancy

AU - Miller, William H.

N1 - Funding Information: This work has been supportedb y the Director, Office of Energy Research,O ffice of Basic Energy Sciences, Chemical SciencesD ivision of the US Departmento f Energy under Contract No. DE-AC03-76SF00098. Support of the Berkeley Theoretical Chemistry Computational Facility by National Science Foundation Grant CHE8C16345 is gratefully acknowledged.

PY - 1988/10/7

Y1 - 1988/10/7

N2 - The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated "improved" ones) is not correct through first order in the time increment Δt. The correct result for the phase (i.e. the action) of the short time propagator is developed in this paper as a power series in Δt, explicit expressions being given for the terms of order Δt-1, Δt, and Δt3. Test applications to the standard harmonic oscillator and also to a double well potential (typical for intramolecular H-atom transfer) show the first-order propagator (i.e. the correct result through order Δt) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).

AB - The most commonly used short time propagator in a discretized Feynman path integral (and also several more sophisticated "improved" ones) is not correct through first order in the time increment Δt. The correct result for the phase (i.e. the action) of the short time propagator is developed in this paper as a power series in Δt, explicit expressions being given for the terms of order Δt-1, Δt, and Δt3. Test applications to the standard harmonic oscillator and also to a double well potential (typical for intramolecular H-atom transfer) show the first-order propagator (i.e. the correct result through order Δt) to be a significant improvement over previous ones; inclusion of the third-order term gives considerable additional improvement (i.e. faster convergence).

UR - http://www.scopus.com/inward/record.url?scp=0002328137&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002328137&partnerID=8YFLogxK

U2 - 10.1016/0009-2614(88)80058-7

DO - 10.1016/0009-2614(88)80058-7

M3 - Article

AN - SCOPUS:0002328137

SN - 0009-2614

VL - 151

SP - 1

EP - 8

JO - Chemical Physics Letters

JF - Chemical Physics Letters

IS - 1-2

ER -

Correct short time propagator for Feynman path integration by power series expansion in Δt

Abstract

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this