Natural coordinates for electrons in solids

FEB 01, 1970

The adage that solving a physics problem is a question of finding the right coordinate system is demonstrated for electrons in crystals. Coordinates that reflect the regularity of the crystal greatly simplify the problem.

DOI: 10.1063/1.3021962

Joshua Zak

THE DESCRIPTION OF A PROBLEM in physics can often be significantly simplified by a suitable choice of coordinates. Usually the choice of the best coördinates is dictated by the symmetry of the problem. Thus for a spherically symmetric potential it is most convenient to use spherical coordinates. In some cases it is very easy to choose the right coordinates; in other cases, the problem is not trivial at all. Here we will discuss the choice of suitable coördinates for the motion of electrons in solids.

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References

1. P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, New York, N.Y. (1958).
2. L. D. Landau, E. M. Lifshitz, Quantum Mechanics, Pergamon Press, London (1958).
3. C. Kittel, Quantum Theory of Solids, John Wiley & Sons, New York, N.Y. (1963).
4. J. Zak, Phys. Rev. Lett. 19, 1385 (1967); https://doi.org/PRLTAO
J. Zak, Phys. Rev. 168, 686 (1968).https://doi.org/PHRVAO
5. L. D. Landau, E. M. Lifshitz, Statistical Physics, Pergamon Press, London (1958).
6. J. Zak, Physics Letters (to be published);
Phys. Rev. (to be published).
7. J. Zak, Phys. Rev. 177, 1151 (1969).https://doi.org/PHRVAO

More about the authors

Joshua Zak, Technion, Haifa.