### Abstract

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 language | English |
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Pages (from-to) | 599-604 |

Number of pages | 6 |

Journal | Journal of Chemical Physics |

Volume | 106 |

Issue number | 2 |

Publication status | Published - 8 Jan 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*106*(2), 599-604.

**Dimensional perturbation theory for Regge poles.** / Germann, Timothy C.; Kais, Sabre.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 106, no. 2, pp. 599-604.

}

TY - JOUR

T1 - Dimensional perturbation theory for Regge poles

AU - Germann, Timothy C.

AU - Kais, Sabre

PY - 1997/1/8

Y1 - 1997/1/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001056898&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001056898&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001056898

VL - 106

SP - 599

EP - 604

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 2

ER -