Abstract
The ground state of the H +2 molecule is studied using the equations of classical mechanics and the Einstein quantum condition, J ζ+J μ = h, where J ζ and J μ 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>4a 0. The greatest error comes at R eq and results from the coalesence of two classically allowed regions where the electron can exist.
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Pearson, R. G.: Proc. Nat. Acad. Sci. 78, 4002 (1981)
Bohr, N.: Philos. Mag. 25, 10 (1913); for a recent account see Kragh, H.: J. Chem. Ed. 54, 208 (1977)
Pauli, W.: Dissertation, Munich, 1921, Ann. Physik 68, 177 (1922)
Hill, E. L., Erickson, H. A.: Phys. Rev. 75, 29 (1949)
Strand, M. P., Reinhardt, W. P.: J. Chem. Phys. 70, 3812 (1979)
Born, M.: Mechanics of the atom, pp. 240–246. New York: Ungar Publishing, 1960
Einstein, A.: Verh. Dtsch. Phys. Ges. 19, 82 (1917)
Slater, J. C.: J. Chem. Phys. 1, 87 (1933)
Wind, H.: J. Chem. Phys. 42, 2371 (1965)
Keller, J. B.: Ann. Phys. (N.Y.) 4, 180 (1958); Maslov, Théorie der Perturbations, Paris: Dunod 1972
Leopold, J. G., Percival, I. C.: J. Phys. B13, 1025 (1980)
Miller, S. C., Good, R. H.: Phys. Rev. 91, 174 (1953)
Ford, K. W., Hill, D. L., Wheeler, J. A.: Ann. Phys. (New York) 7, 239 (1959)
Child, M. S.: J. Mol. Spectrosc. 53, 280 (1974)
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Pearson, R.G. The hydrogen molecule ion in the old quantum theory. Theoret. Chim. Acta 64, 127–136 (1983). https://doi.org/10.1007/BF00550327
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DOI: https://doi.org/10.1007/BF00550327