Question 4

Assessment IV . Solve the differential equation 55 (cc) = 9(55') with boundary conditions f(0) = 0, f(1) = 0 using Green's mction method. . Show that the wave equation in 2dimensions does not have a propagating solution. . Show using power counting method that Green function of the Poissson's equation is not divergent in three dimensions. [+00 dw eiiwr not, 271' (w2 czkz)' The two poles of this integral can be displaced by an innitesimal imag- inary part it's so as to lie either in the upper or lower half plane. This leads to four possible ways of making the divergent integral nite: The limit .5 > 0 taken after the integral is evaluated, gives nite boundary values. Find these values. . Consider the integral: . Assuming the integral 1 x/s2+k:2 ' nd Im(f0 dkeiCTWkR for CW R2. f dice-Swami) = D