The Green’s Functions of the Helmholtz Equation and Their Applications

  • Eugen Skudrzyk


The solution of a partial differential equation for a periodic driving force or source of unit strength that satisfies specified boundary conditions is called the Green’s function of the specified differential equation for the specified boundary conditions. Thus, the Green’s function represents the effect of a unit source or force at any point of the system (called force point) on the field at the point of observation (called observation or field point).


Wave Equation Real Axis Helmholtz Equation Field Point Unit Source 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Franz, W.: Über die Greenschen Funktionen des Zylinders und der Kugel. Z. Naturf. 9a (1954) 705 716.MathSciNetADSGoogle Scholar
  2. Imai, I.: Die Beugung elektromagnetischer Wellen an einem Kreiszylinder. Z. Physik 137 (1954) 31 48.MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. Lanczos, C.: Linear differential operators. Princeton, N. J.: D. van Nostrand. 1961.Google Scholar
  4. Morse, P. M., Feshbach, H.: Methods of theoretical physics, Vol. I and II. New York, N. Y.: McGraw-Hill. 1953.Google Scholar
  5. Morse, P. M., Ingard, K. U.: Theoretical acoustics. New York, N. Y.: McGraw-Hill. 1968;Google Scholar
  6. Morse, P. M., Ingard, K. U.: Linear acoustic theory, in Handbuch d. Physik, Vol. XI/1 Akustik, p. 1–127. Berlin Göttingen—Heidelberg: Springer. 1961.Google Scholar
  7. Rudnick, I.: The propagation of an acoustic wave along a boundary. J.A.S.A. 19 (1947) 348–356.MathSciNetGoogle Scholar
  8. Sommerfeld, A.: Über die Ausbreitung der Wellen in der drahtlosen Telegraphie. Ann. Physik 28 (1909) 665–736;ADSzbMATHCrossRefGoogle Scholar
  9. Sommerfeld, A.: Partial differential equations in physics. New York, N. Y.: Academic Press. 1949.Google Scholar
  10. Stakgold, I.: Boundary value problems of mathematical physics, Vol. II. London: Macmillan. 1968.Google Scholar
  11. Stratton, J. A.: Electromagnetic theory. New York, N. Y.: McGraw-Hill. 1941.Google Scholar
  12. Weyl, H.: Ausbreitung elektromagnetischer Wellen über einen ebenen Leiter. Ann. Physik 60 (1919) 481 500.ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Eugen Skudrzyk
    • 1
  1. 1.Ordnance Research Laboratory and Physics DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations