Abstract
This chapter concerns two problems. First, we consider the Helmholtz formula which enables us to express the field at any point of some region through boundary values of this field and its normal derivative. Section 3.1 presents a simple derivation of the Helmholtz formula when it directly follows from the differentiation rule for discontinuous functions. The advantage of this derivation is a clear demonstration of the Helmholtz formula ambiguity which is used in the following chapters. Section 3.1 also discusses some consequences of the formula and derives integral equations for surface density at the boundary.
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© 1999 Springer-Verlag Berlin Heidelberg
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Voronovich, A. (1999). Helmholtz Formula and Rayleigh Hypothesis. In: Wave Scattering from Rough Surfaces. Springer Series on Wave Phenomena, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59936-1_3
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DOI: https://doi.org/10.1007/978-3-642-59936-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64187-9
Online ISBN: 978-3-642-59936-1
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