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Expansion technique for crystal surface problems
1.M. J. Gottlieb, Am. J. Math. 60, 453 (1938). The Gottlieb polynomials are a special case of the more general Meixner polynomials,
1.see Joseph Meixner, J. London Math. Soc. 9, 6 (1934).
2.For a discussion of several types of orthogonal polynomials of a discrete variable, see G. Szegö, Orthogonal Polynomials, Am. Math. Soc. Colloq. Publications 23 (Am. Math. Soc., Providence, R. I., 1959), rev. ed.
3.A. A. Maradudin, R. F. Wallis, D. L. Mills, and R. L. Ballard, Phys. Rev. B 6, 1106 (1972);
3.S. L. Moss, A. A. Maradudin, and S. L. Cunningham, Phys. Rev. B 8, 2999 (1973);
3.T. M. Sharon, A. A. Maradudin, and S. L. Cunningham, Phys. Rev. B 8, 6024 (1973);
3.T. M. Sharon and A. A. Maradudin, Sol. State Comm. 13, 187 (1973).
4.R. F. Wallis, A. A. Maradudin, I. P. Ipatova, and A. A. Klochikhin, Solid State Comm. 5, 89 (1967).
5.For this particular wave vector an exact analytic solution is obtainable by recognizing the fact that layers 1, 3, 5,⋯decouple from layers 0, 2, 4, ⋯, with the consequence that the spins in layers 1, 3, 5, ⋯are stationary. The spin wave amplitude for the even‐numbered layers decays with depth as a pure exponential and has a frequency which agrees (for ) with the converged value in Table I. I am grateful to J. Dobson for pointing out the existence of this analytic solution.
6.Investigations are currently underway concerning their use in low energy electron diffraction (LEED) intensity calculations and also in calculations of the surface band structure of transition metals.
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