Lattice Harmonics I. Cubic Groups

S. L. ALTMANN; A. P. CRACKNELL

doi:10.1103/RevModPhys.37.19

Access by Xinjiang University

Lattice Harmonics I. Cubic Groups

S. L. ALTMANN and A. P. CRACKNELL^*

Department of Metallurgy, Oxford University, Oxford, England

^*Present address: Department of Physics, University of Singapore, Singapore 10, Malaysia.

PDF

Rev. Mod. Phys. 37, 19 – Published 1 January, 1965

DOI: https://doi.org/10.1103/RevModPhys.37.19

Abstract

A review is given of some conventions and definitions required for the derivation of the irreducible representations of the space groups, and of a method to obtain lattice harmonics. These are given for all the irreducible representations of the simple cubic ( $Pm 3 m$ ), face-centered cubic ( $Fm 3 m$ ) and body-centered cubic ( $Im 3 m$ ) space groups for $l \leq 12$ . The expansions are given in polar coordinates and care has been taken that different bases corresponding to the same representation span identical, rather than equivalent, representations, which are given in full. Moreover, all the different expansions listed in the tables are fully orthogonal.

References (15)

F. C. von der Lage and H. A. Bethe, Phys. Rev. 71, 612 (1947)
F. S. Ham, Phys. Rev. 128, 82 (1962)
D. G. Bell, Rev. Mod. Phys. 26, 311 (1954)
M. A. Melvin, Rev. Mod. Phys. 28, 18 (1956)
S. L. Altmann, Proc. Cambridge Phil. Soc. 53, 343 (1957)
S. L. Altmann and C. J. Bradley, Phil. Trans. London A255, 199 (1963)
S. L. Altmann, Proc. Roy. Soc. (London) A244, 141 (1958)
S. L. Altmann, "Group Theory" in Quantum Theory, edited by D. R. Bates (Academic Press Inc., New York, 1962), Vol. II, p. 144
E. P. Wigner, Group Theory (Academic Press Inc., New York, 1959)
F. Seitz, Ann. Math. 37, 17 (1936)
C. Herring, J. Franklin Inst. 233, 525 (1942)
L. P. Bouckaert, R. Smoluchowski, and E. Wigner, Phys. Rev. 50, 58 (1936)
G. F. Koster, Solid State Phys. 5, 174 (1957)
D. F. Johnston, Rept. Progr. Phys. 23, 66 (1960)
S. L. Altmann, Phil. Trans. Roy. Soc. London A255, 216 (1963)

[c1] F. C. von der Lage and H. A. Bethe, Phys. Rev. 71, 612 (1947)

[c2] F. S. Ham, Phys. Rev. 128, 82 (1962)

[c3] D. G. Bell, Rev. Mod. Phys. 26, 311 (1954)

[c4] M. A. Melvin, Rev. Mod. Phys. 28, 18 (1956)

[c5] S. L. Altmann, Proc. Cambridge Phil. Soc. 53, 343 (1957)

[c6] S. L. Altmann and C. J. Bradley, Phil. Trans. London A255, 199 (1963)

[c7] S. L. Altmann, Proc. Roy. Soc. (London) A244, 141 (1958)

[c8] S. L. Altmann, "Group Theory" in Quantum Theory, edited by D. R. Bates (Academic Press Inc., New York, 1962), Vol. II, p. 144

[c9] E. P. Wigner, Group Theory (Academic Press Inc., New York, 1959)

[c10] F. Seitz, Ann. Math. 37, 17 (1936)

[c11] C. Herring, J. Franklin Inst. 233, 525 (1942)

[c12] L. P. Bouckaert, R. Smoluchowski, and E. Wigner, Phys. Rev. 50, 58 (1936)

[c13] G. F. Koster, Solid State Phys. 5, 174 (1957)

[c14] D. F. Johnston, Rept. Progr. Phys. 23, 66 (1960)

[c15] S. L. Altmann, Phil. Trans. Roy. Soc. London A255, 216 (1963)

Reviews of Modern Physics

Export citation

Export citation

Lattice Harmonics I. Cubic Groups

Abstract

References (15)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation