-- use rectangular coordinates r = sqrt(x^2 + y^2 + z^2) F = exp(i k r) / r "Verify equation (1)" A = dot(grad(1/r),grad(exp(i k r))) B = div(grad(exp(i k r))) / r C = exp(i k r) div(grad(1/r)) check(div(grad(F)) == 2 A + B + C) "ok" "Verify equation (2)" check(A == -i k exp(i k r) / r^2) "ok" "Verify equation (3)" check(B == 2 i k exp(i k r) / r^2 - k^2 exp(i k r) / r) "ok" -- verify for nonzero r "Verify equation (4)" check(div(grad(F)) == -k^2 F) "ok" Run