  Although free electron models have been established in order to capture the
essential physics of interfacial and bulk properties in metals, some issues
still remain regarding the application of free electron models to thin metal
films. One of the issues relates to whether the geometric edge coincides with
the potential edge in order to satisfy the charge neutrality condition when the
potential profile is modeled as a rectangular potential well. We show that they
coincide by rigorously taking into account the quantization effect arising from
electron confinement in a thin metal slab. As a result, the overall behaviors
of the chemical potential and surface energy show an increasing trend by
decreasing the thickness of the slab. The chemical potential and surface energy
show an oscillatory thickness dependence by further taking into account the
discreteness of the total number of free electrons.
