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

Published online by Cambridge University Press:  15 September 2014

Ian Sandeman
Ian Sandeman
Affiliation:
University of St Andrews
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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∑.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 55 , 1936 , pp. 49 - 61
Copyright
Copyright © Royal Society of Edinburgh 1936

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References

References to Literature

Brillouin, L., 1926. “La méchanique ondulatoire de Schrödinger; une méthode générale de résolution par approximations successives,” C.R. Acad. Sci. Paris, T. clxxxiii, p. 24.Google Scholar
Dunham, J. L., 1932. “The Wentzel-Brillouin-Kramers Method of Solving the Wave Equation,” Phys. Rev., vol. xli, p. 713; “The Energy Levels of a Rotating Vibrator,” Phys. Rev., p. 721.CrossRefGoogle Scholar
Fues, E., 1926. “Das Eigenschwingungsspektrum zweiatomiger Moleküle in der Undulationsmechanik,” Ann. Phys., Leipzig, Bd. lxxx, p. 367.CrossRefGoogle Scholar
Gale, H. G., Monk, G. S., and Lee, K. O., 1928. “Wave-lengths in the Secondary Spectrum of Hydrogen,” Astrophys. Journ., vol. lxvii, p. 89.CrossRefGoogle Scholar
Kramers, H. A., 1926. “Wellenmechanik und halbzahlige Quantisierung,” Zeits. Phys., Bd. xxxix, p. 828.CrossRefGoogle Scholar
Kratzer, K., 1922. “Die Gesetzmässigkeit der Bandensysteme,” Ann. Phys., Leipzig, Bd. lxvii, p. 127.CrossRefGoogle Scholar
Morse, P. M., 1929. “Diatomic Molecules according to the Wave Mechanics. II. Vibrational Levels,” Phys. Rev., vol. xxxiv, p. 57.CrossRefGoogle Scholar
Richardson, O. W., and Das, K., 1929. “The Spectrum of H2: The Bands Analogous to the Ortho-helium Line Spectrum,” pt. i, Proc. Roy. Soc., A, vol. cxxii, p. 688; pt. ii, Proc. Roy. Soc., vol. cxxv, p. 312.Google Scholar
Richardson, O. W., and Davidson, P. M., 1929 a. “The Spectrum of H2: The Bands Analogous to the Parhelium Line Spectrum,” pt. i, Proc. Roy. Soc., A, vol. cxxiii, p. 54; pt. ii, Proc. Roy. Soc., vol. cxxiii, p. 466; pts. iii and iv, Proc. Roy. Soc., vol. cxxiv, p. 50.Google Scholar
Richardson, O. W., and Davidson, P. M., 1929 b. “The Energy Functions of the H2 Molecules,” Proc. Roy. Soc., A, vol. cxxv, p. 23.Google Scholar
Sandeman, I., 1929. “The Fulcher Bands of Hydrogen,” Proc. Roy. Soc. Edin., vol. xlix, p. 48.Google Scholar
Sandeman, I., 1933. “The Mathematical Representation of the Energy Levels of the Secondary Spectrum of Hydrogen,” Proc. Roy. Soc. Edin., vol. liii. p. 347.Google Scholar
Wentzel, G., 1926. “Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik,” Zeits. Phys., Bd. xxxviii, p. 518.CrossRefGoogle Scholar