The WKB approximation. It does not reduce to the rectangular barrier correctly while the transfer matrix method does. The connection between the rectangular barrier and potentials of arbitrary shape is less transparent for the WKB than the transfer matrix method. It can be more difficult than the transfer matrix method. It's less accessible to undergraduates.
Students are unfamiliar with numerical methods, but are well acquainted with matrix operations.
Classroom Results 1. The method is accessible. Undergraduates can do it. Matrix operations are familiar. The student response is good.