Solving the potential barrier smoothness conditions for relationships among the coefficients A, B, and F, giving the reflection and transmission probabilities, usually involves rather messy algebra. However, there is a special case that can be done fairly easily, though requiring a slight departure from the standard solutions used in the chapter. Suppose the incident particles’ energy E is precisely U0. (a) Write down solutions to the Schrodinger equation in the three regions. Be especially careful in the region 0<x<L. It should have two arbitrary constants, and it isn’t difficult—just different. (b) Obtain the smoothness conditions, and from these, find R and T. (c) Do the results snake sense in the limit L→ ∞?
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