Problem.Set.2 - g t t 2 g t t t t(b In the case that the...

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Problem Set 2 : 2.1 The Coulomb potential for a point charge located at r 0 is given by r,r 0 q | r r 0 | a) Find 2 r,r 0 and write down the partial differential equation satisfied by r,r 0 . b) Using steps similar to those found on page 12 of Chapter 1 for the wave equation, find the fourier transform, k,r 0 ), of the Coulomb potential. c) Find k,r 0 directly from r,r 0 1 2 3  k,r 0 exp i k r d 3 k d) Evaluate the following integral 0 sin ku du 2.2 The ‘displacement’ of a damped, harmonic oscillator satisfies the equation x   x   0 2 x f t . (a) Obtain the Green’s function for this equation. That is, find g t t such that g t t
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Unformatted text preview: g t t 2 g t t t t (b) In the case that the ‘force’ is given by f t f t t exp t / and x 0, x 0 evaluate x t . (c) Let 0.1 and evaluate the energy (per unit mass) supplied by the force in the time interval from to . Plot this energy, divided by the final energy stored by the oscillator, as a function of ln from 0.01 to 100....
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