Reflection of waves from varying media
Author:
C. O. Hines
Journal:
Quart. Appl. Math. 11 (1953), 9-31
MSC:
Primary 36.0X
DOI:
https://doi.org/10.1090/qam/54130
MathSciNet review:
54130
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Abstract: Formulae are found for the coefficient of reflection from varying media of a type encountered in physics. These are applied approximately for some general classes of media, and exactly for some specific cases. Many media which would normally be expected to be highly reflecting are shown to be completely transparent to certain waves at least and, in some cases, to a whole spectrum of waves. The results are considered both for electromagnetic (or other classical) waves and for mass waves.
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Lord Rayleigh, On the propagation of waves through a stratified medium, with special reference to the question of reflection, Proc. Roy. Soc. A 86, 207–226 (1912).
L. Brillouin, La mécanique ondulatoire de Schrödinger; une méthod générale de résolution par approximations successives, Comptes Rendus 183, 24–26 (1926).
G. Wentzel, Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik, Zeits. f. Physik 38, 518–529 (1926).
H. A. Kramers, Wellenmechanik und halbzahlige Quantisierung, Zeits. f. Physik 39, 828–840 (1926).
E. C. Kemble, A contribution to the theory of the B. W. K. method, Phys. Rev. 48, 549–561 (1935).
E. C. Kemble, The fundamental principles of quantum mechanics, McGraw-Hill Book Company, Inc., New York, 1937, sec. 21.
R. E. Langer, The asymptotic solutions of certain linear ordinary differential equations of the second order, Trans. Amer. Math. Soc. 36, 90–106 (1934).
R. E. Langer, The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to the Stokes phenomenon, Bull. Amer. Math. Soc. 40, 545–582 (1934).
R. E. Langer, On the connection formulas and the solutions of the wave equation, Phys. Rev. 51, 669–676 (1937).
W. H. Furry, Two notes on phase-integral methods, Phys. Rev. 71, 360–371 (1947).
C. Eckart, The penetration of a potential barrier by electrons, Phys. Rev. 35, 1303–1309 (1930).
P. S. Epstein, Reflection of waves in an inhomogeneous absorbing medium, Nat. Acad. Sci. 16, 627–637 (1930).
O. E. Rydbeck, On the propagation of waves in an inhomogeneous medium, Trans. Chalmers U., Gothenburg, Sweden, Nr. 74 (1948).
G. Gamow, Zur Quantentheorie des Atomkernes, Zeits. f. Physik 51, 204–212 (1928).
L. Brillouin, Wave propagation in periodic structures, McGraw-Hill Book Company, Inc., New York, 1946, chap. VIII.
S. A. Schelkunoff, Remarks concerning wave propagation in stratified media, Communications on Pure and Applied Mathematics 4, 117–128 (1951).
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Article copyright:
© Copyright 1953
American Mathematical Society
