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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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Full Text: DOI

References:

[1] Mathieu, É., J. Math. Pures Appl. Sér. 2, 13, 137-203 (1868)
[2] Hill, G. W., Acta Math., 8, 1-36 (1886) · JFM 18.1106.01
[3] Eastham, M. S.P., The Spectral Theory of Periodic Differential Equations (1974), Hafner: Hafner New York · Zbl 0285.34015
[4] Reed, M.; Simon, B., (Methods of Modern Mathematical Physics, Vols. I-IV (1972-1979), Academic Press: Academic Press New York), (especially Vol. IV) · Zbl 0242.46001
[5] Goldstein, S., (Proc. Roy. Soc. Edinburgh, 49 (1929)), 210-223 · JFM 55.0260.02
[6] Harrell, E., Commun. Math. Phys., 60, 73-95 (1978) · Zbl 0395.34023
[7] S. Coleman; S. Coleman
[8] Kato, T., J. Phys. Soc. Japan, 4, 334-339 (1949)
[9] Harrell, E., (Proc. Amer. Math. Soc., 69 (1978)), 271-276 · Zbl 0345.47007
[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: North-Holland Amsterdam · Zbl 0129.41907
[12] Berry, M. V.; Mount, K. E., Rep. Prog. Phys., 35, 315-397 (1972)
[13] E. Harrell and B. Simon; E. Harrell and B. Simon
[14] Whittaker, E. T.; Watson, G. N., A Course of Modern Analysis (1969), Cambridge Univ. Press: Cambridge Univ. Press London · Zbl 0108.26903
[15] (Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions. Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series, Vol. 55 (1964), National Bureau of Standards: National Bureau of Standards Washington) · Zbl 0171.38503
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