Reflection off a reflecting surface in quantum mechanics: where do the reflections actually occur

A detailed analytical study is carried out of the problem for the reflection of a particle off a reflecting surface in quantum mechanics. It is used the method of Green's functions with suitable boundary conditions. A careful analysis is made to know where the reflections actually occur on the reflecting surface. In particular, it is shown that the reflecting surface is equivalent to a purely geometrical imaginary surface which merely ''constraints'' the possible quantum-mechanical ''paths'' of a particle on or above it