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Show that a pulsed spherical wave has a complex wavefunction of the form U(r,t) = (1/r)a(t-r/c) where a(t) is an arbitrary function. An ultrashort optical pulse has a complex wavefunction with a central frequency corresponding to a wavelength λ0 = 585nm and a Gaussian envelope of rms width σ1 = 6fs. How many cycles are contained within the pulse width? If the pulse propagates in free space as a spherical wave initiated at the origin at t = 0, describe the spatial distribution of the intensity as a function of the radial distance at time t = 1ps.
What are the basic analytical frameworks of modern economics? The fundamental analytical framework of modern economics: The fundamental analytical framework for an econom
A monopolist faces the following demand function for its product: Q = 45 - 5P The fixed costs of the monopolist are $12 and the variable costs are $5 per unit. a) What are the
using the basic Keynesian model answewr the following parts carefully using the relevant diagrams. what happens to the equilibrium level of GDP(Y) given the following: a) a reducti
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Relation between TP and MP: Graphically, given the total product curve, MP is the slope of the tangent at any point on the TP curve. This is shown in Figure. See that
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For each of following production functions, comment on the ability to substitute capital for labor. Note that Q, K, and L denote output, capital, and labor respectively. A: B
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