### Abstract

The problem of determining the total wave functions and energies of molecular stationary states reduces to solving a Schrödinger equation with a vibrational-rotational Hamiltonian. This is achieved by a unitary transformation of the molecular Hamiltonian H with its successive diagonalization on a nondegenerate electronic state |e〉. It is shown that the molecular wave functions related to the electronic states |e〉 are of the form G|e〉|g〉_{(e)}, and their corresponding energy value is the sum e{open}_{e} + e{open}_{g}^{(e)}, where e{open}_{g}^{(e)} and |g〉^{(e)} are the eigenvalues and eigenfunctions of the vibrational-rotational Hamiltonian, determined by means of the unitary operator G. It is shown that the total energy and molecular wave functions are uniquely determined, despite the arbitrariness in choosing G. As an example the vibrational-rotational operator and molecular wave functions are given for the simplest choice of the operator G.

Original language | English |
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Pages (from-to) | 299-303 |

Number of pages | 5 |

Journal | Soviet Physics Journal |

Volume | 18 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 1975 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Soviet Physics Journal*,

*18*(3), 299-303. https://doi.org/10.1007/BF00889286

**Partial diagonalization in solving electron-nuclear problems in molecules.** / Makushkin, Yu S.; Ulenikov, O. N.

Research output: Contribution to journal › Article

*Soviet Physics Journal*, vol. 18, no. 3, pp. 299-303. https://doi.org/10.1007/BF00889286

}

TY - JOUR

T1 - Partial diagonalization in solving electron-nuclear problems in molecules

AU - Makushkin, Yu S.

AU - Ulenikov, O. N.

PY - 1975/3/1

Y1 - 1975/3/1

N2 - The problem of determining the total wave functions and energies of molecular stationary states reduces to solving a Schrödinger equation with a vibrational-rotational Hamiltonian. This is achieved by a unitary transformation of the molecular Hamiltonian H with its successive diagonalization on a nondegenerate electronic state |e〉. It is shown that the molecular wave functions related to the electronic states |e〉 are of the form G|e〉|g〉(e), and their corresponding energy value is the sum e{open}e + e{open}g(e), where e{open}g(e) and |g〉(e) are the eigenvalues and eigenfunctions of the vibrational-rotational Hamiltonian, determined by means of the unitary operator G. It is shown that the total energy and molecular wave functions are uniquely determined, despite the arbitrariness in choosing G. As an example the vibrational-rotational operator and molecular wave functions are given for the simplest choice of the operator G.

AB - The problem of determining the total wave functions and energies of molecular stationary states reduces to solving a Schrödinger equation with a vibrational-rotational Hamiltonian. This is achieved by a unitary transformation of the molecular Hamiltonian H with its successive diagonalization on a nondegenerate electronic state |e〉. It is shown that the molecular wave functions related to the electronic states |e〉 are of the form G|e〉|g〉(e), and their corresponding energy value is the sum e{open}e + e{open}g(e), where e{open}g(e) and |g〉(e) are the eigenvalues and eigenfunctions of the vibrational-rotational Hamiltonian, determined by means of the unitary operator G. It is shown that the total energy and molecular wave functions are uniquely determined, despite the arbitrariness in choosing G. As an example the vibrational-rotational operator and molecular wave functions are given for the simplest choice of the operator G.

UR - http://www.scopus.com/inward/record.url?scp=34250384844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250384844&partnerID=8YFLogxK

U2 - 10.1007/BF00889286

DO - 10.1007/BF00889286

M3 - Article

VL - 18

SP - 299

EP - 303

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 3

ER -