Algebraic Determination of Spectral Characteristics of Rovibrational States of Diatomic Molecules. I. Diagram Technique for Determination of Vibrational Dependences of Matrix Elements

Research output: Contribution to journalArticle

Abstract

Explicit algebraic expressions for the expansion of the vibrational matrix elements in series of matrix elements on the wave functions of the ground vibrational state have been obtained for arbitrary sufficiently differentiable functions of the internuclear distance, arbitrary values v and v', and the potential curves whose ladder operators can be constructed. A diagram technique have been developed for it that consists in: 1) the numeration of the matrix elements by points of the 2D diagram with coordinates (l, k), 2) the drawing arrows between points of this diagram corresponding to the action of the annihilation operators on the wave functions; 3) total taking into account of all possible path vectors formed by the continuous sequences of arrows from point (v, v) towards points (0, k). The only requirement is that the action of the operator on the wave functions should give the wave functions of the Schroedinger equation with the potential curve having the same parameter values. All necessary data for alge
Original languageUndefined
Pages (from-to)1-17
JournalarXiv
Issue number1112.6409
StatePublished - 2011

Keywords

  • vibrational matrix elements
  • algebraic methods
  • ladder operators
  • diagram technique

Cite this