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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 is the difference between 'scarcity' and 'shortage'? 'Scarcity' and 'shortage' have dissimilar definitions. In reality, when most of the goods and resources are scarce go
a) Microeconomics is concerned with decision-making within the firm, household or on the individual level, but macroeconomics is concerned with the behavior of the whole economic s
introduction of production
Q. What do you mean by Externality? An externality exists when the actions of one individual affect the wellbeing of other individuals without any compensation taking place. F
Consider an economy with high innovative potential, but where saving is insufficient to fund innovative investments. Use Garrison's capital-based macroeconomics to explain how more
The following model shows the consumption function given: Ct = AD t β 2 Where A and β 2 are unknown constants and D is disposable income. (a) Show how by taking logari
Recent developments in demand theory
what is break even quantity
Explain how the price system eliminates a surplus. The meaning of surplus is that quantity demanded is less as compared to the quantity supplied. This will lead to downward pr
(i) When the demand function is 2Q - 24 + 3P = 0, find the marginal revenue when Q=3. (ii) Given the demand function 0.1Q - 10 +0.2P + 0.02P2 =0, calculate the price elasticity of
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