- Access by Xinjiang University
Localized Functions in Molecules and Crystals
Phys. Rev. 89, 67 – Published 1 January, 1953
DOI: https://doi.org/10.1103/PhysRev.89.67
Abstract
The Wannier function in crystals is defined in terms of a differential equation and a variation procedure. This variation procedure is also used to define localized functions in molecules which can be used to build solutions of Schrödinger's equation. Illustrations of the procedure of building solutions of Schrödinger's equation from localized functions is given for examples taken from crystalline and molecular problems. Contact is made with Slater's work on the two-dimensional Mathieu problem. A numerical method of carrying out the variation procedure is discussed.
References (15)
- G. H. Wannier, Phys. Rev. 52, 191 (1937)
- Eyring, Walter, and Kimball, Quantum Chemistry (John Wiley and Sons, Inc., New York, 1947), p. 172-189 E. Wigner, Gruppentheorie (Friedr. Vieweg und Sohn, Braunschweig, 1931) A. Speiser Die Theorie der Gruppen (Julius Springer, Berlin, 1927)
Omitted endnote
- F. Bloch, Z. Physik 52, 555 (1928)
Omitted endnote
Omitted endnote
Omitted endnote
- F. BlochQuantum Chemistry, p. 179 ([2])
- F. Seitz, Z. Krist. 88, 433 (1934) ibid.90, 289 (1935) ibid.91, 336 (1935) ibid.94, 100 (1936)
Omitted endnote
- F. Seitz, Ann. Math. 37, 17 (1936)
- Bouckaert, Smoluchowski, and Wigner, Phys. Rev. 50, 58 (1936)
- J. C. Slater, Phys. Rev. 87, 807 (1952)
- P. O. Löwdin, Phys. Rev. 18, 365 (1950)
- J. E. Lennard-Jones, Proc. Roy. Soc. (London) A198, 14 (1949)