An ultra-short optical pulse has a complex wave-function with a... | Filo
An ultra-short optical pulse has a complex wave-function with a... | Filo
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SOLVED: Show that for the complex amplitude U(r) of the complex wavefunction U(F,t) = U(r)e^(iwt) (1), the Helmholtz equation (V^2 k^2)U(r) = 0 (2) is fulfilled, where V^2 denotes the Laplace operator and k = w/c is the wavenumber. Verify that the complex amplitude of the spherical wave U(r) = -ikr (3), with A and r being the wave's amplitude and distance from the origin, respectively, satisfies the Helmholtz equation. Derive an expression for the intensity I of a spherical wave (Equation (3))
SOLVED: Show that for the complex amplitude U(r) of the complex wavefunctio…
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