Many attempts were made to derive with the old quantum theory structures for the hydrogen molecule, H₂, and the hydrogen molecule-ion, H₂^+, in agreement with the experimentally observed properties of these substances, in particular their energy contents. These were all unsuccessful, as were similar attempts to derive a satisfactory structure for the helium atom. It became increasingly evident that in these cases the straightforward application of the old quantum theory led to results definitely incompatible with the observed properties of the substances, and that the introduction of variations in the quantum rules was not sufficient to remove the disagreement. (For a summary of these applications see, for example, Van Vleck (1). ) This fact was one of those which led to the rejection of the old quantum theory and the origination of the new quantum mechanics. The fundamental principles of the quantum mechanics were proposed by Heisenberg (2) in 1925. The introduction of the matrix algebra (3) led to rapid developments. Many applications of the theory were made, and in every case there was found agreement with experiment. Then the wave equation was discovered by Schrodinger (4), who developed, and applied his wave mechanics independently of the previous work. Schrodinger’s methods are often considerably simpler than matrix methods of calculation, and since it has been shown (5) that the wave mechanics and the matrix mechanics are mathematically identical, the wave equation is generally used as the starting point in the consideration of the properties of atomic systems, in particular of stationary states.
Linus Pauling (1928) studied this question.