VII.—The Mathematical Representation of the Energy Levels of the Secondary Spectrum of Hydrogen.—III

Abstract

In a recent communication (Sandeman, 1935) some problems arising out of the attempt to obtain accurate values of the molecular constants in applying the results of the wave mechanics to the secondary spectrum of hydrogen have been discussed, and an analysis of the two molecular states Is2s3∑ and Is2p1∑ on the basis of Dunham's (1932) solution of the Schrödinger equation for the molecular rotating vibrator has been carried out and compared with the previous calculations of Richardson and Davidson and Richardson and Das. In the present paper an analysis of the ground state (IsIs1∑) of the hydrogen molecule—made possible by recent advances in the measurement and allocation of the band lines —has been attempted. For comparison a similar analysis of the ground state of the molecular ion H2+(Is2∑) is included. Although the spectrum of the molecular ion is not known, the fact that the variables in the Schrödinger equation are separable enables an analysis to be built up from theoretical considerations.