Reflection-Refraction at an n1-n2 Junction and Stable Equilibrium Like Conditions?

The problem of a photon reflecting or refracting at an n1-n2 index of refraction is solved in (1) using the notion of continuity of the electric field of a photon and its d/dx derivative for the n1-n2 junction at x=0. The photon electric field behaves as cos(-wt+kx) or cos(-Et+px). We argue first of all that the photon is a quantum object and that this problem is really a quantum mechanical one as it may also be solved for a particle with rest mass using two different constant potentials V1, V2 instead of n1,n2. In this note, we consider the photon case for convenience. Given that the problem is really a quantum mechanical one (in our opinion), we ask: How far can one go by trying to solve it classically? We first point out that for a static uniform arrangement of objects in space, P(x)dx =dx/L, where L is an arbitrary length. In the case of particles moving at constant v, one may argue that each particle spends the same amount of time dt in each dx and that this also leads to a constant density in space. We suggest that for this to hold, one must consider a steady state problem and the notion of flux for physical reasons. This leads to writing the equation 1= Probability(reflect)+Probability(refract) as AA/c = BB/c + CC/c2 where AA, BB, CC are the incident, reflected and refracted fluxes and c1=c, c2=c/n2. We have shown in previous notes that one may mathematically write this single equation as: A+B=C and Ap-Bp = Cp2 using E=pc (with E the same for the incident, reflected and refracted photon) and then solve the two equations for the two unknowns B,C, setting A=1. This approach yields a result which matches experiment, but from the standpoint of classical physics, there is no a priori reason to take the square root of flux. It simply arises as a math trick so to speak, we argue, and there seems to be no physical motivation. Here, we suggest approaching the problem differently. We note that if c1-c2