Effect of Multiple Reflections in a Multilayer of a Normal Metal and a Superconductor

We derive a set of equations to study the transport properties for a multilayer of a normal metal (N) and a superconductor (S) in the ballistic region. We apply the general equations to compute the local density of states and the current density for an NSN layer while varying the thickness of the layer and the transmission coefficient of the interface. The interference of particles reflected from the interfaces in the superconducting layer leads to a resonance phenomenon in the density of states and the current density. The normalization condition of the quasiclassical theory is violated due to the interference. Our formalism also enables us to find an analytic expression for the Andreev reflection coefficient of the NSN layer.