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Phase velocity#,v_p = omega/k#
#therefore omega = v_pk#
Group velocity #,v_g = (domega)/(dk#
#v_g = (d(v_pk))/(dk)#
#= v_p (dk)/(dk) + k(dv_p)/(dk)#
#v_p + (2pi)/lambda (dv_p)/(d((2pi)/lambda))#
#v_p + 1/lambda(dv_p)/(d((1)/lambda))#
#v_p + 1/lambda(dv_p)/(d((1)/lambda))(dlambda)/(dlambda)#
#"But " d/(dlambda^-1) = -lambda^2#
#therefore v_g = v_p - lambda (dv_p)/(dlambda)#
if #v_p = c_1 + c_2lambda#
then #v_g = c_1 + c_2lambda - lambda (d(c_1 + c_2lambda))/(dlambda)#
#= c_1 + c_2lambda - lambda(0+c_2)#
#= c_1 + c_2lambda - c_2lambda#
#v_g = c_1#