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Theoretica chimica acta

, Volume 64, Issue 2, pp 127–136 | Cite as

The hydrogen molecule ion in the old quantum theory

  • Ralph G. Pearson
Original Investigations

Abstract

The ground state of the H 2 + molecule is studied using the equations of classical mechanics and the Einstein quantum condition, Jζ+Jμ = h, where Jζ and Jμ are the action integrals over a complete cycle of the elliptic coordinates. Strong bonding is found, but the quantitative results are good only for R<0.05 and R>4a0. The greatest error comes at R eq and results from the coalesence of two classically allowed regions where the electron can exist.

Key words

Old quantum theory Bohr-Sommerfeld theory Quantum condition 

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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Ralph G. Pearson
    • 1
  1. 1.Department of ChemistryUniversity of CaliforniaSanta BarbaraUSA

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