A FIG.1:Maupertuis'Principle. Here we make comparison between light propagation of monochromatic light wave and wave propagation of monochromatic matter wave Light wave geometric optics Fermat's principle wave propagationHelmholtz equation Matter waveparticle dynamics Principle of least action wave propagation Presently unknown Now consider light wave propagation in a non-homogeneous medium light path= hn()ds Fermat's principle 6n问ds=0 For a particle moving in a potential field V(,the principle of least action reads 5amns=6v6me-阿w=0 The corresponding light wave equation (Helmholtz equation)is (-)0=0 which after the separation of variables reduces to + Here we note that w is a constant.Thus we arrived at a result of comparison as follows 5A B FIG. 1: Maupertuis’ Principle. Here we make comparison between light propagation of monochromatic light wave and wave propagation of monochromatic matter wave Light wave geometric optics Fermat’s principle wave propagation Helmholtz equation Matter wave particle dynamics Principle of least action wave propagation Presently unknown Now consider light wave propagation in a non-homogeneous medium light path = Z B A n(~r)ds Fermat’s principle δ Z B A n(~r)ds = 0 For a particle moving in a potential field V (~r), the principle of least action reads δ Z B A √ 2mT ds = δ Z B A p 2m(E − V (~r))ds = 0 The corresponding light wave equation (Helmholtz equation) is µ ∇2 − 1 c 2 ∂ 2 ∂t2 ¶ u (~r, t) = 0 which after the separation of variables reduces to ∇2ψ + n 2ω 2 c 2 ψ = 0. Here we note that ω is a constant. Thus we arrived at a result of comparison as follows 5