V.—The Mathematical Representation of the Energy Levels of the Secondary Spectrum of Hydrogen.—II.

Abstract

In a recent paper (Sandeman, 1933) the question of the mathematical representation of the energy levels of the hydrogen molecule by methods based on the old mechanics has been considered. In view of the fact that the wave mechanics has supplanted the older theory, the further application of newer methods to this spectrum is desirable. Richardson and Davidson (1929 b, p. 45) worked out the potential energy function U(ξ) (ξ is denned on p. 51) for the state IsσЗpπ3Π on the old quantum mechanics and on the wave mechanics with the following results: U(ξ) = 5·50ξ2(1 – 1·556ξ + 1·58ξ2 – 1·56ξ3) volts on the old quantum mechanics and U(ξ) = 5·71ξ2(1 – 1·55ξ + 1·58ξ2 – 1·59ξ3) volts on the wave mechanics. They also (loc. cit., pp. 30 and 31) gave the U(ξ)'s for the states Isσ2pσ1∑, Isσ2sσ3∑, and IsσЗdπ1Πb, and on p. 45 they gave the formulæ, based on Fues's (1926) results, for transcribing the old quantum mechanics into the wave mechanics series. Richardson and Das (1929, pt. ii) gave similar data for the state IsσЗpσ3∑.