Knowledge Bank

The case of a threefold degenerate vibrational state is more complex due to the Coriolis interaction between the degenerate vibration and the rotation; important contributions were made to this problem by II. A. Jahn, J. D. Louck and K. T. Hecht, using symmetry considerations. However new secular equations had to be solved, each time a new band or a new molecule was studied. We propose a method where the secular equations can be solved numerically once for all. It is then possible to use explicit formulae expressing the wave numbers of the lines as functions of quantum numbers and molecular parameters. This method has been applied to the fundamental $\nu 4$ of methane.