Exponential power series expansion for the quantum time evolution operator

Nancy Makri, William H. Miller

Research output: Contribution to journalArticlepeer-review


The coordinate matrix element of the time evolution operator, exp[ -iĤt/ℏ], is determined by expanding (its exponent) in a power series in t. Recursion relations are obtained for the expansion coefficients which can be analytically evaluated for any number of degrees of freedom. Numerical application to the tunneling matrix element in a double well potential and to the reactive flux correlation function for a barrier potential show this approach to be a dramatic improvement over the standard short time approximation for the propagator. Its use in a Feynman path integral means that fewer "time slices" in the matrix product exp[ ( -i/ℏ) ΔtĤ]N, Δt = t/N, will be required. The first few terms in the present expansion constitute a fully quantum version of the short time propagator recently obtained by us using semiclassical methods [Chem. Phys. Lett. 151, 1 (1988)].

Original languageEnglish (US)
Pages (from-to)904-911
Number of pages8
JournalThe Journal of Chemical Physics
Issue number2
StatePublished - 1989
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry


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