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The band-structure of a one-dimensional, periodic system in a scaling limit. (English) Zbl 0412.34013

MSC:
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
34L99 Ordinary differential operators
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
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[1] Mathieu, É., J. math. pures appl. Sér. 2, 13, 137-203, (1868)
[2] Hill, G.W., Acta math., 8, 1-36, (1886)
[3] Eastham, M.S.P., The spectral theory of periodic differential equations, (1974), Hafner New York · Zbl 0285.34015
[4] Reed, M.; Simon, B., (), (especially Vol. IV)
[5] Goldstein, S., (), 210-223
[6] Harrell, E., Commun. math. phys., 60, 73-95, (1978)
[7] {\scS. Coleman}, “The Uses of Instantons,” 1977 Ettore Majorana International School of Subnuclear Physics Lectures, in press.
[8] Kato, T., J. phys. soc. Japan, 4, 334-339, (1949)
[9] Harrell, E., (), 271-276
[10] Simon, B., Ann. phys. (N.Y.), 58, 76-136, (1970)
[11] Fröman, N.; Fröman, P.O., JWKB approximation, contributions to the theory, (1965), North-Holland Amsterdam · Zbl 0129.41907
[12] Berry, M.V.; Mount, K.E., Rep. prog. phys., 35, 315-397, (1972)
[13] {\scE. Harrell and B. Simon}, to appear.
[14] Whittaker, E.T.; Watson, G.N., A course of modern analysis, (1969), Cambridge Univ. Press London · Zbl 0108.26903
[15] ()
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