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Date of Publication:2002-01-01

Journal:物理学报

Affiliation of Author(s):物理学院

Volume:51

Issue:5

Page Number:1026-1030

ISSN No.:1000-3290

Abstract:The electronic states of a linear molecule are the eigen-vectors of the
   projectional component of electron's angular momentum operator along the
   direction of the molecular axis, because the molecular axis is a
   symmetric axis of the Hamiltonian of the linear molecule. If an
   electronic energy eigen-state has a non-zero eigen-value of the angular
   momentum, the state would be a double-degenerated state, which is
   composed of two states that have respectively reverse eigen-values of
   the angular momentum. Due to something of coupling effect in the
   molecule, the degenerated doublet of the electronic state splits into
   two states, which have different eigen-values of energy and reverse
   eigen-valuers of the angular momentum. The coupling of electron angular
   momentum and molecule rotation momentum plays the most important role in
   the splitting of the doublet of the electronic state. But the coupling
   of these two kinds of angular momentum, in essence, is a result of the
   entanglement between the movement of electrons and molecular frame, not
   real coupling interaction of the two angular momenta. In this paper,
   classic dynamics is first used to study the rotation of a linear
   molecule as a rigid rotor with a fixed attached angular momentum and
   Euler's and Lagrange's equations for the rotation of the linear molecule
   has been deduce. After constructing an extensive potential function to
   equations of the rotation of the linear molecule are both achieved. The
   Hamilton function has been foune to be regular quadratic, and therefore
   the correlative Hamiltonian for the rotation of the linear molecule is
   also obtained by complying with Bohr's correspondence principle and the
   construction rules of operator in quantum theory. The Hamiltonian has
   also been re-written into two parts as J. H. Van. Vleck has done and the
   resultant expressions are exactly the same as J. H. Van. Vleck's famous
   result. But the deduction in the paper is much more explicit than that
   of J. H. Van. Vleck.

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