(a) (6 marks) Given the advanced and retarded Green functions (CH denotes Heaviside's step function) Dret (x) = _04(xo)S

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A 6 Marks Given The Advanced And Retarded Green Functions Ch Denotes Heaviside S Step Function Dret X 04 Xo S 1 (91.28 KiB) Viewed 19 times

(a) (6 marks) Given the advanced and retarded Green functions (CH denotes Heaviside's step function) Dret (x) = _04(xo)S(22), ( Dadv(2) = Dret (-x), = 1 27 give the expression for a retarded and an advanced solution of the same inhomoge- nous wave equation. Explain the physical picture behind these solutions and why the advanced Green function is not much used in classical electrodynamics. (b) (6 marks) Use the above expression for the retarded Green's function to show that the solution of the wave equation for the 4-vector potential (where f(x) = (41/C) x 3"(x) in Gaussian units) can be written in the form: 1 A"(20) = Sex! diz]"(ctret, x') (1) x - x' with tret = t - x - x'\/c, the retarded time. (c) (8 marks) Starting from Eq. (1) show that the Lorentz gauge, O.A"(x) = 0 is satisfied.
-0,844(x) = f(x) can be solved using a Green's function 0,04D(x) = $(4) (2)