Soviet Physics Journal

, Volume 18, Issue 3, pp 299–303 | Cite as

Partial diagonalization in solving electron-nuclear problems in molecules

  • Yu. S. Makushkin
  • O. N. Ulenikov


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 ɛe + ɛg(e), where ɛ 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.


Wave Function Total Energy Stationary State Electronic State Unitary Operator 
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Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Yu. S. Makushkin
    • 1
  • O. N. Ulenikov
    • 1
  1. 1.Institute of Atmospheric OpticsSiberian Branch of the Academy of Sciences of the USSRUSSR

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