Formalism of quantum number polynomials

Theoretical aspects of the recent perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. By the example of a biatomic molecule, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Hermann-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established. ©2005 Springer Science+Business Media, Inc.