Addition theorems for spherical wave functions
Author:
Seymour Stein
Journal:
Quart. Appl. Math. 19 (1961), 15-24
MSC:
Primary 33.00
DOI:
https://doi.org/10.1090/qam/120407
MathSciNet review:
120407
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Abstract: Addition theorems are described for spherical vector wave functions, under both rotations and translations of the coordinate system. These functions are the characteristic solutions in spherical coordinates of the vector wave equation, such as occurs in electromagnetic problems. The vector wave function addition theorems are based on corresponding theorems for the spherical scalar wave functions. The latter are reviewed and discussed.
- William Sterling Ament, WAVE PROPAGATION IN SUSPENSIONS, ProQuest LLC, Ann Arbor, MI, 1959. Thesis (Ph.D.)–Brown University. MR 2612877
J. Stratton, Electromagnetic theory, McGraw-Hill, N. Y., 1941, p. 414 ff.
Ibid., p. 404–406
Ibid., p. 401
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
A. Erdelyi, et al., Higher transcendental functions, vol. 2, McGraw-Hill, N. Y., 1953 Chap. 11, esp. p. 257
Y. Sato, Transformation of wave-functions related to transformations of coordinate systems, Bull. Earthquake Research Inst. Tokyo 28, 1–22 and 175–217 (1950)
H. Hönl, Über ein Additionstheorem der Kugelfunktionen und seine Anwendung auf die Richtungsquantisierung der Atome, Z. Physik 89, 244–253 (1934)
A. Schmidt, Formeln zur Transformation der Kugelfunktionen bei linearer ÄAnderung des Koordinaten-systems, Z. Math. Phys. 44, 327–338 (1899)
H. McIntosh, A. Kleppner, and D. F. Minner, Tables of the Herglotz polynomials of orders 3/2, 8/2, transformation coefficients for spherical harmonics, BRL Memo., Rept. No. 1097, July 1957, Ballistic Research Laboratories, Aberdeen Proving Ground, Md.
- A. R. Edmonds, Angular momentum in quantum mechanics, Investigations in Physics, Vol. 4, Princeton University Press, Princeton, N.J., 1957. MR 0095700
Ibid., p. 24
Ibid., p. 6–8
Ibid., p. 61, Eq. 4.3.4, with ${j_1} = 1$
J. S. Lamont, Applications of finite groups, Academic Press, N. Y., 1959, p. 150–151
Reference 11, p. 61, Eq. 4.3.2. with ${j_1} = 1$
Reference 10, p. 21, in which the formulas are correct for the $U_{kl}^n$ , rather than the $H_{kl}^m$ as written; also p. 19
- Bernard Friedman and Joy Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12 (1954), 13–23. MR 60649, DOI https://doi.org/10.1090/S0033-569X-1954-60649-8
- Arnold Sommerfeld, Partial Differential Equations in Physics, Academic Press, Inc., New York, N. Y., 1949. Translated by Ernst G. Straus. MR 0029463
Reference 11, p. 45 ff., also Eqs. 4.6.5, 3.7.5, 3.7.3, 3.6.10, 3.6.11, 3.1.5
Reference 11, p. 48–50, and p. 95
W. S. Ament, Wave propagation in suspensions, NRL Rept. 5307, April 9, 1959
J. Stratton, Electromagnetic theory, McGraw-Hill, N. Y., 1941, p. 414 ff.
Ibid., p. 404–406
Ibid., p. 401
R. Courant and D. Hilbert, Methods of mathematical physics, vol. 1, Interscience, N. Y., 1953, Appendix to Chap. 7, by W. Magnus
A. Erdelyi, et al., Higher transcendental functions, vol. 2, McGraw-Hill, N. Y., 1953 Chap. 11, esp. p. 257
Y. Sato, Transformation of wave-functions related to transformations of coordinate systems, Bull. Earthquake Research Inst. Tokyo 28, 1–22 and 175–217 (1950)
H. Hönl, Über ein Additionstheorem der Kugelfunktionen und seine Anwendung auf die Richtungsquantisierung der Atome, Z. Physik 89, 244–253 (1934)
A. Schmidt, Formeln zur Transformation der Kugelfunktionen bei linearer ÄAnderung des Koordinaten-systems, Z. Math. Phys. 44, 327–338 (1899)
H. McIntosh, A. Kleppner, and D. F. Minner, Tables of the Herglotz polynomials of orders 3/2, 8/2, transformation coefficients for spherical harmonics, BRL Memo., Rept. No. 1097, July 1957, Ballistic Research Laboratories, Aberdeen Proving Ground, Md.
A. R. Edmonds, Angular momentum, in quantum mechanics, Princeton Univ. Press, Princeton, N. J., 1957, Chap. 4
Ibid., p. 24
Ibid., p. 6–8
Ibid., p. 61, Eq. 4.3.4, with ${j_1} = 1$
J. S. Lamont, Applications of finite groups, Academic Press, N. Y., 1959, p. 150–151
Reference 11, p. 61, Eq. 4.3.2. with ${j_1} = 1$
Reference 10, p. 21, in which the formulas are correct for the $U_{kl}^n$ , rather than the $H_{kl}^m$ as written; also p. 19
B. Friedman and J. Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12, 13–23 (1954)
E.g., A. Sommerfeld, Partial differential equations, Academic Press, N. Y., 1949, p. 128–129
Reference 11, p. 45 ff., also Eqs. 4.6.5, 3.7.5, 3.7.3, 3.6.10, 3.6.11, 3.1.5
Reference 11, p. 48–50, and p. 95
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Article copyright:
© Copyright 1961
American Mathematical Society