Answer Happy

Please be careful to use basic conditions and equations toderive wave equations separately. Thank you.
Basic equations in some matter are written by rotE(x,t)+∂t∂B​(x,t)=0divB(x,t)=0∫−∞∞​dωeiωtμ(ω)1​[rotB~(x,ω)−v2(ω)iω​E~(x,ω)]=0​ ∫−∞∞​dωeiωtϵ(ω)divE~(x,ω)=0 where D(x,t)=∫−∞∞​D~(x,ω)eiωt dω,E(x,t)=∫−∞∞​E~(x,ω)eiωt dωD~(x,ω)=ϵ(ω)E~(x,ω).(B~(x,ω)=μ(ω)H~(x,ω) as well )​
Using the potentials and the Lorenz gauge condition, E(x,t)=−∂t∂A′​(x,t)−gradϕ′(x,t)B(x,t)=rotA′(x,t)divA~′(x,ω)+v2(ω)iω​ϕ~​′(x,ω)=0​ derive the wave equations for A~′(x,ω) and ϕ~​′(x,ω).