Wave Mechanics and the Normal State of the Hydrogen Molecule
E. U. Condon
The problem of the motion of a particle attracted by two fixed centers of force according to the Coulomb force law can be treated by classical mechanics and has been used in quantum theory by Pauli and Messen for a theory of the hydrogen molecule ion.1 In the quantum mechanics, where the energy levels are determined as the “eigenwerte” of Schrodinger’s equation, the variables are separable and the boundary value problem is easily set up. But thus far a satisfactory treatment of the differential equations involved is lacking. Burrau2 has recently carried out a numerical integration of the problem for the lowest energy level of an electron moving under the influence of two fixed centers of Coulomb attraction as a function of the distance apart of these centers. In this paper, Burrau’s data are used to give a semi-quantitative discussion of the neutral hydrogen molecule. His values are:
Nuclear separation
1.0
1.3
1.6
1.8
2.0
2.2
2.4
2.95
Electronic energy
2.896
2.648
2.436
2.309
2.204
2.109
2.025
1.836
The unit of separation is the Bohr l1 orbit radius of hydrogen atom, that of energy is the ionization potential of atomic hydrogen.
Proceedings of the National Academy of Sciences•Jun 1, 1927•38 citations