An alternative derivation of (almost-) Watson’s Hamiltonian

Abstract

A derivation of the general wave-mechanical Hamiltonian for non-linear molecules is presented. It is based on the transformation of proper classical (Hamilton) moment into their wave-mechanical counterparts by means of the Podolsky transformation in its original form. The result is essentially identical to that obtained by Watson in his milestone paper [J.K.G. Watson, Mol. Phys. 15 (1968) 479]. While not so elegant as that of the original reference, the way proposed in the present study is conceptually much simpler. This procedure can be applied to other types of molecular Hamiltonians too.