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Equivalent functions: hybrids and Wannier functions

Published online by Cambridge University Press:  24 October 2008

S. L. Altmann  and
C. A. Coulson
S. L. Altmann
Affiliation:
Mathematical Institute‡Oxford
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Extract

In the last two decades a family of closely related functions have been introduced for the solution of quantum-mechanical problems. In dealing with atomic and molecular systems Pauling (12) introduced in 1928 linear combinations of the eigenfunctions of a single atom, which were called hybrids. These have specific symmetry properties which were utilized by Kimball (6) to construct a group-theoretical method for their determination. More recently Lennard-Jones (8) defined linear combinations of molecular eigenfunctions which he called equivalent orbitals. These are formally similar to the hybrids and Lennard-Jones took over the Kimball method for their determination.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 197 - 206
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCES

(1)Altmann, S. L.Band structure, theory and experiment. Proceedings of a symposium held at R.R.E., p. 51 (Malvern, 1954).Google Scholar
(2)Altmann, S. L.Proc. Camb. Phil. Soc. 53 (1957), 343.CrossRefGoogle Scholar
(3)Bloch, F.Z. Phys. 52 (1929), 555.CrossRefGoogle Scholar
(4)Courant, B. and Hilbert, D.Methods of mathematical physics, vol. I (New York, 1953).Google Scholar
(5)Hall, G. G.Proc. Roy. Soc. A, 202 (1950), 341.Google Scholar
(6)Kimball, G.J. Chem. Phys. 8 (1940), 188.CrossRefGoogle Scholar
(7)Koster, G. F.Phys. Rev. 89 (1953), 67.Google Scholar
(8)Lennard-Jones, J.Proc. Roy. Soc. A, 198 (1949), 1, 14.Google Scholar
(9)Löwdin, P. O.Phys. Rev. 18 (1950), 365.Google Scholar
(10)Löwdin, P. O.Advanc. Phys. 5 (1956), 1.CrossRefGoogle Scholar
(11)Parzen, G.Phys. Rev. 89 (1953), 237.CrossRefGoogle Scholar
(12)Pauling, L.Proc. Nat. Acad. Sci., Wash., 14 (1928), 359.CrossRefGoogle Scholar
(13)Slater, J. C.Phys. Rev. 87 (1952), 807.CrossRefGoogle Scholar
(14)Wannier, G.Phys. Rev. 52 (1937), 191.CrossRefGoogle Scholar
(15)Winston, H.Phys. Rev. 94 (1954), 328.CrossRefGoogle Scholar
(16)Wigner, E.Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atom-spektren (Braunschweig, 1931).CrossRefGoogle Scholar