A new approach to the molecular rotational hamiltonian

The present paper is devoted to a new approach of the rotational hamiltonian of a non degenerate vibronic state of the semi-rigid molecules. It is based upon two points. Firstly the hermitian operators on a finiten dimensional vector space belong to an ² dimensional euclidian vector space. Secondly, the vector space of the rotational states is a direct sum of irreducible representations of the rotation group. Accordingly in each one of those representations the rotational hamiltonian can be represented by its set of real components on a orthonormal basis of hermitian operators. The components of the reduced hamiltonian of Watson limited to its quartic terms are determined.