Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] William Sterling Ament, WAVE PROPAGATION IN SUSPENSIONS, ProQuest LLC, Ann Arbor, MI, 1959. Thesis (Ph.D.)–Brown University. MR 2612877
  • [2] J. Stratton, Electromagnetic theory, McGraw-Hill, N. Y., 1941, p. 414 ff.
  • [3] Ibid., p. 404-406
  • [4] Ibid., p. 401
  • [5] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [6] A. Erdelyi, et al., Higher transcendental functions, vol. 2, McGraw-Hill, N. Y., 1953 Chap. 11, esp. p. 257
  • [7] Y. Sato, Transformation of wave-functions related to transformations of coordinate systems, Bull. Earthquake Research Inst. Tokyo 28, 1-22 and 175-217 (1950)
  • [8] H. Hönl, Über ein Additionstheorem der Kugelfunktionen und seine Anwendung auf die Richtungsquantisierung der Atome, Z. Physik 89, 244-253 (1934)
  • [9] A. Schmidt, Formeln zur Transformation der Kugelfunktionen bei linearer ÄAnderung des Koordinaten-systems, Z. Math. Phys. 44, 327-338 (1899)
  • [10] 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.
  • [11] A. R. Edmonds, Angular momentum in quantum mechanics, Investigations in Physics, Vol. 4, Princeton University Press, Princeton, N.J., 1957. MR 0095700
  • [12] Ibid., p. 24
  • [13] Ibid., p. 6-8
  • [14] Ibid., p. 61, Eq. 4.3.4, with $ {j_1} = 1$
  • [15] J. S. Lamont, Applications of finite groups, Academic Press, N. Y., 1959, p. 150-151
  • [16] Reference 11, p. 61, Eq. 4.3.2. with $ {j_1} = 1$
  • [17] 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
  • [18] Bernard Friedman and Joy Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12 (1954), 13–23. MR 0060649, https://doi.org/10.1090/S0033-569X-1954-60649-8
  • [19] Arnold Sommerfeld, Partial Differential Equations in Physics, Academic Press, Inc., New York, N. Y., 1949. Translated by Ernst G. Straus. MR 0029463
  • [20] 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
  • [21] Reference 11, p. 48-50, and p. 95

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 33.00

Retrieve articles in all journals with MSC: 33.00


Additional Information

DOI: https://doi.org/10.1090/qam/120407
Article copyright: © Copyright 1961 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website