Publisher： Elsevier
ISSN： 0003-4916
Source： Annals of Physics, Vol.255, Iss.1, 1997-03, pp. : 75-96
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Abstract
It is shown that any Hamiltonian involving only one- and two-bond interactions for a molecule with n bonds and having a point group P as its symmetry group may have the S n⊃ P partial dynamical symmetry, i.e., the Hamiltonian can be solved analytically for a part of the states, called the unique states. For example, the XY 6 molecule has the S 6⊃ O h partial dynamical symmetry. The model of Iachello and Oss for n coupled anharmonic oscillators is revisited in terms of the partial dynamical symmetry. The energies are obtained analytically for the nine unique levels of the XY 6 molecule and the structures of the eigenstates are disclosed for the first time, while for non-unique states they are obtained by diagonalizing the Hamiltonian in the S 6⊃ O h symmetry adapted basis with greatly reduced dimension.
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