  The reflection and transmission of wave functions at a potential step is a
well-known issue in a textbook of quantum mechanics. We studied the reflection
and transmission characteristics analytically when the potential step is moving
at a constant velocity $v$ in the same direction as an incident wave function
by means of solving the time-dependent Schr\"{o}dinger equation. As for an
infinite potential step, it is known that group velocity is the same as the
moving velocity of the potential step. We found two interesting results when
the potential step has a finite height of $V_0$. The transmission occurs when
the kinetic energy of incident wave function is larger than the effective
potential hight of $(\sqrt{\frac{m}{2}}v + \sqrt{V_0})^2$. The other result is
that the reflectivity depends on $x$, which derives from the interference
between the incident and the reflected wave functions.
