  In this paper, we calculate the transmission and reflection amplitudes of
wave functions for different potentials such as the delta function, the
rectangular barrier, the Eckart potential, and the Hulthen potential. We
describe the relationship between these amplitudes and compute the reflection
resonances between each potential. We describe the transmission and reflection
probabilities using the WKB formula and compare the results with ones obtained
from matching the boundary conditions. Furthermore, we use a two by two
transfer matrix to calculate a rigorous bound on the transmission and
reflection probabilities.
