A Note on the One-Electron States of Diatomic Molecules

The explicit formulation of an integral of the motion is given for a single electron moving in the field of two fixed nuclei, for both the classical and the quantum mechanical cases. The corresponding quantal operator together with the Schrödinger Hamiltonian and the operator for the component of the orbital angular momentum of the electron about the internuclear axis form a complete set of commuting observables of the problem. This supplies the dynamical interpretation of the separation parameter of the energy equation.