### Abstract

The form of the effective Hamiltonian of a quantum system with allowance for corrections of arbitrary order for solving arbitrary quantum-mechanical problems with perturbation operator depending not only on the same coordinates as the operator of the zero approximation, but also on an arbitrary set of other coordinates whose derivative operators may not commute with each other, is retrieved based on the operator perturbation theory (the recurrence formulas for corrections of any arbitrary order of the operator perturbation theory are presented in the paper in the most general form). The general results obtained allow the special features of the effective operators of any polyatomic molecule to be investigated. As a first step, an arbitrary diatomic molecule is investigated. Isotopic relations among different spectroscopic parameters are derived for the parent molecule and its various isotopic modifications.

Original language | English |
---|---|

Pages (from-to) | 500-507 |

Number of pages | 8 |

Journal | Russian Physics Journal |

Volume | 58 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 2015 |

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### Keywords

- diatomic molecules
- isotopic relationships
- operator perturbation theory

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Russian Physics Journal*,

*58*(4), 500-507. https://doi.org/10.1007/s11182-015-0527-4

**Study of Spectroscopic Properties of Diatomic Molecules Based on High Orders of the Operator Perturbation Theory.** / Bekhtereva, E. S.; Litvinovskaya, A. G.; Konov, I. A.; Gromova, O. V.; Chertavskikh, Yulia; Tse, Yang Fang; Ulenikov, O. N.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 58, no. 4, pp. 500-507. https://doi.org/10.1007/s11182-015-0527-4

}

TY - JOUR

T1 - Study of Spectroscopic Properties of Diatomic Molecules Based on High Orders of the Operator Perturbation Theory

AU - Bekhtereva, E. S.

AU - Litvinovskaya, A. G.

AU - Konov, I. A.

AU - Gromova, O. V.

AU - Chertavskikh, Yulia

AU - Tse, Yang Fang

AU - Ulenikov, O. N.

PY - 2015/8

Y1 - 2015/8

N2 - The form of the effective Hamiltonian of a quantum system with allowance for corrections of arbitrary order for solving arbitrary quantum-mechanical problems with perturbation operator depending not only on the same coordinates as the operator of the zero approximation, but also on an arbitrary set of other coordinates whose derivative operators may not commute with each other, is retrieved based on the operator perturbation theory (the recurrence formulas for corrections of any arbitrary order of the operator perturbation theory are presented in the paper in the most general form). The general results obtained allow the special features of the effective operators of any polyatomic molecule to be investigated. As a first step, an arbitrary diatomic molecule is investigated. Isotopic relations among different spectroscopic parameters are derived for the parent molecule and its various isotopic modifications.

AB - The form of the effective Hamiltonian of a quantum system with allowance for corrections of arbitrary order for solving arbitrary quantum-mechanical problems with perturbation operator depending not only on the same coordinates as the operator of the zero approximation, but also on an arbitrary set of other coordinates whose derivative operators may not commute with each other, is retrieved based on the operator perturbation theory (the recurrence formulas for corrections of any arbitrary order of the operator perturbation theory are presented in the paper in the most general form). The general results obtained allow the special features of the effective operators of any polyatomic molecule to be investigated. As a first step, an arbitrary diatomic molecule is investigated. Isotopic relations among different spectroscopic parameters are derived for the parent molecule and its various isotopic modifications.

KW - diatomic molecules

KW - isotopic relationships

KW - operator perturbation theory

UR - http://www.scopus.com/inward/record.url?scp=84956926899&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956926899&partnerID=8YFLogxK

U2 - 10.1007/s11182-015-0527-4

DO - 10.1007/s11182-015-0527-4

M3 - Article

AN - SCOPUS:84956926899

VL - 58

SP - 500

EP - 507

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 4

ER -