Helmholtz equation spherical wave solution

In a collection scattered photons will be emitted in all directions, and the atoms will appear to be acting (approximately) as secondary sources of spherical waves. The spherical wave solution to the Helmholtz equation gives an electric field, E,(r,t), dependent upon the distance, r, between the point of observation, P, and a source located at the origin, according to ... [Pg.3]

Monochromatic Waves (1.14) A monochromatic e.m. wave Vcj r,t) can be decomposed into the product of a time-independent, complex-valued term Ucj r) and a purely time-dependent complex factor expjojt with unity magnitude. The time-independent term is a solution of the Helmholtz equation. Sets of base functions which are solutions of the Helmholtz equation are plane waves (constant wave vector k and spherical waves whose amplitude varies with the inverse of the distance of their centers. [Pg.278]

The spherical wave functions form a set of characteristic solutions to the Helmholtz equation and are given by [215]... [Pg.261]

This well-known Helmholtz wave equation has two linearly independent solutions which we may take to be the spherical Bessel j (Kr) and Neumann n (Kr) functions, respectively. From the small Kr limits... [Pg.67]

The spherical vector wave functions (SVWF) are the general solution of the vectorial Helmholtz differential equation in spherical coordinates (Xu 1995) ... [Pg.337]

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