Dimensional perturbation theory for Regge poles

Timothy C. Germann, Sabre Kais

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We apply dimensional perturbation theory to the calculation of Regge pole positions, providing a systematic improvement to earlier analytic first-order results. We consider the orbital angular momentum l as a function of spatial dimension D for a given energy E, and expand l in inverse powers of κ≡(D-1)/2. It is demonstrated for both bound and resonance states that the resulting perturbation series often converges quite rapidly, so that accurate quantum results can be obtained via simple analytic expressions given here through third order. For the quartic oscillator potential, the rapid convergence of the present l(D;E) series is in marked contrast with the divergence of the more traditional E(D;l) dimensional perturbation series, thus offering an attractive alternative for bound state problems.

Original languageEnglish
Pages (from-to)599-604
Number of pages6
JournalJournal of Chemical Physics
Issue number2
Publication statusPublished - 8 Jan 1997


ASJC Scopus subject areas

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

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