Sommerfeld Identity
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High Quality Content by WIKIPEDIA articles! The Sommerfeld identity is a mathematical identity, due Arnold Sommerfeld, used in the theory of propagation of waves, frac{{e^{ik R} }} {R} = intlimits_0^infty I_0(lambda r) e^{ - mu left z right } frac{{lambda d lambda}}{{mu}} where mu = sqrt {lambda ^2 - k^2 } is to be taken with positive real part, to ensure the convergence of the integral and its vanishing in the limit z rightarrow pm infty and R2 = r2 + z2. Here, R is the distance from the origin while r is the distance from the central axis of a cylinder as in the (r, ,z) cylindrical…mehr

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High Quality Content by WIKIPEDIA articles! The Sommerfeld identity is a mathematical identity, due Arnold Sommerfeld, used in the theory of propagation of waves, frac{{e^{ik R} }} {R} = intlimits_0^infty I_0(lambda r) e^{ - mu left z right } frac{{lambda d lambda}}{{mu}} where mu = sqrt {lambda ^2 - k^2 } is to be taken with positive real part, to ensure the convergence of the integral and its vanishing in the limit z rightarrow pm infty and R2 = r2 + z2. Here, R is the distance from the origin while r is the distance from the central axis of a cylinder as in the (r, ,z) cylindrical coordinate system. The function I0 is a Bessel function. Here the notation for Bessel functions follows the German convention, to be consistent with the original notation used by Sommerfeld.