Abstract
Many problems in solid state theory consist in solving the time-independent Schrödinger equation
to obtain the energy eigenvalues E n together with the corresponding eigenfunctions ψ n . Since one is dealing with a large number of particles (~1023 electrons + nuclei) a solution of this many-particle problem can only be obtained after various approximations and simplifications. Without going into detail we shall simply mention the usual approximations made in solving Schrödinger’s equation:
-
(i)
Since our main interest is in the electronic system, we separate the motion of electrons and nuclei and consider the latter as being fixed (Born-Oppenheimer approximation). This approximation of course is invalid if we are interested in finite temperature effects. It is, however, in most cases sufficient to treat finite temperature effects, like electron-phonon coupling by perturbation.
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(ii)
The remaining many-electron problem can be reduced to a one-electron problem by defining an averaged potential, like the Hartree or Hartree-Fock potential. Exchange and correlation can be treated in several local or non-local approximations according to their importance in the particular problem. The resulting one-electron potential can be iterated in a self-consistent way until convergence is reached.
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(iii)
Spin and other relativistic effects are usually introduced through the standard two-component Pauli matrix formalism. This approximation of Dirac’s treatment is valid in the low energy region we are concerned with.
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References
E. P. Wigner: Group Theory and Its Application to Quantum Mechanics, Academic Press, New York 1959.
M. Tinkham: Group Theory and Quantum Mechanics, McGraw Hill, New York 1964.
L. M. Falicov: Group Theory and Its Physical Applications, University Press, Chicago 1972.
M. I. Petrashen and E. D. Trifonov: Applications of Group Theory in Quantum Mechanics, Cambridge 1969.
V. Heine: Group Theory in Quantum Mechanics, Pergamon Press, Oxford 1966.
G. F. Koster: Space Groups and Their Representations, Academic Press, New York 1957.
M. Lax: Symmetry Principles in Solid State and Molecular Physics, Wiley, New York 1974.
F. Bassani and G. Pastori-Parravicini: Electronic States and Optical Transitions in Solids, Pergamon Press, Oxford 1975.
G. F. Koster, J. O. Dimmock, R. G. Wheeler, and H. Statz: Properties of the Thirty-Two Point Groups, MIT Press, Cambridge 1969.
C. Herring: J. Franklin Inst. 233 (1942), 525.
R. J. Elliott and R. Loudon: J. Phys. Chem. Solids, 15 (1960), 146.
J. Zak:. J. Math. Phys. 1 (1960), 165.
H. W. Streitwolf: Deut. Akad. Wiss. Berlin, Veróff. Phys.-Techn. Inst., 1962.
J. C. Slater: Quantum Theory of Molecules and Solids, McGraw Hill, New York 1965, Vol. 2.
C. Herring: Phys. Rev. 52 (1937), 361.
L. F. Mattheiss, J. H. Wood and A. C. Switendick: in Methods in Computational Physics, ed. by B. Adler, S. Fernbach, M. Rotenberg, Academic Press, New York 1968, Vol. 8.
A. W. Luehrmann: PhD Thesis, Chicago 1968, unpublished.
S. Altmann: Rev. Mod. Phys. 37 (1965), 33.
C. J. Bradley and A. P. Cracknell: The Mathematical Theory of Symmetry in Solids, Clarendon Press, Oxford 1972;
O. V. Kovalev: Irreducible Representations of the Space Groups, Gordon Breach, New York 1968.
B. Renaud and M. Schlüter: Heiv. Phys. Acta, 45 (1972), 66.
R. Zallen and D. F. Blossey: review in the same series.
J. I. Hanoka, K. Vedam and H. K. Henisch: J. Phys. Chem. Solids, Supplement (1967), 369.
A. Kuhn, R. Chevalier and A. Rimsky: Acta Cryst. B32 (1976), 1975.
R. W. G. Wyckoff: Crystal Structures, Wiley, New York 1963, Vols. 1, 2.
J. A. Wilson, F. J. Di Salvo and S. Mahajan: Adv. Phys. 24 (1975), 117.
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© 1979 D. Reidel Publishing Company, Dordrecht, Holland
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Schlüter, M. (1979). Symmetry Considerations. In: Wieting, T.J., Schlüter, M. (eds) Electrons and Phonons in Layered Crystal Structures. Physics and Chemistry of Materials with Layered Structures, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9370-9_1
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DOI: https://doi.org/10.1007/978-94-009-9370-9_1
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