The molecular vibration-rotation hamiltonian

Abstract

By use of commutation relations and sum rules Watson [1] has simplified the Darling and Dennison hamiltonian and obtained The quantity H - U is thus identical to the analytical expression of the classical hamiltonian. By reconsidering completely the question of the derivation of the quantum mechanical hamiltonian we intend to prove that the U term comes only from the particular method chosen to derive the quantum mechanical hamiltonian from its wave mechanical representations. From this we conclude that in the usual model, the quantum mechanical vibration-rotation hamiltonian has the same form as the classical one.