Suppose that N electrons of mass n are placed in a ``box,'' or
infinite square well which contains the particles in the region 0 < x
< L. Suppose that there are three electrons in the box, each
occupying one of the three lowest pure energy states
of the box. Plot the function
, which represents the
average total density of electrons in the box. It turns out
that when N>>1 (many electrons in the box), the oscillations which
you see become quite small and the density appears nearly constant
across the box.