Consider a beam of particles impinging on a potential step of height
with energy 
as shown in Figure 1. The
step in potential occurs over an infinitesimal region of size
at x=0. Note that the force 
must be very large over this small region to produce
the discontinuous change in potential of size .
Figure 1: Upward potential step
In lecture, we derived the following wave function, which is a pure state of energy E shown in the figure:
where N is a normalization constant and
These two latter parameters obey the relationship
.
Note that the step is narrow enough that the wave function has nearly
the constant value 
over the entire range of width
.
