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.