(Green's function for the Three-Dimensional Helmholtz Equation). We consider the three-dimensional wave equation -{4, -c*V*u] =...

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(Green's function for the Three-Dimensional Helmholtz Equation). We consider the three-dimensional wave equation -{4, -c*V*u] = q(r.t), where q(r,t) is a source. If q(r,t) = (r)exp(-ior) represents a source ocillating with a single frequency w, then, as expected, at least after an initial transient period, the entire motion reduces to a wave motion with the same frequency w so that we can write u(r,t)= u(r)exp(-iot). Consequently, the wave equation (1.11.54) reduces to the three-dimensional Helmholtz equation -(v? +k* )u(r) = f(r). (1.11.54) %3D (1.11.55) (Green's function for the Three-Dimensional Helmholtz Equation). We consider the three-dimensional wave equation -{4, -c*V*u] = q(r.t), where q(r,t) is a source. If q(r,t) = (r)exp(-ior) represents a source ocillating with a single frequency w, then, as expected, at least after an initial transient period, the entire motion reduces to a wave motion with the same frequency w so that we can write u(r,t)= u(r)exp(-iot). Consequently, the wave equation (1.11.54) reduces to the three-dimensional Helmholtz equation -(v? +k* )u(r) = f(r). (1.11.54) %3D (1.11.55)