Rectangular Potential Barrier

Rectangular potential barriers, also called square potential barriers, are formed by energy potentials which create wall-like barricades for particles. Essentially, a potential barrier is a potential step except the energy potential returns to zero at some finite positive $x$-position, $a$, and remains zero beyond that point. Here, we'll derive the wave function of a particle facing a rectangular potential barrier, then find the transmission and reflection coefficients of the particle upon encountering the barrier.

Potential Step

Potential steps are created by energy potentials which form step-like barricades for particles. Before the potential step, the energy potential is uniformly zero, but at the step, the energy potential rises instantaneously to a finite value and remains constant at that value for all positions beyond the step. Here, we'll derive the wave function of a particle facing a potential step, then find the transmission and reflection coefficients of the particle upon encountering the step.