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


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
Full Text: DOI


[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] ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.