In class we considered tunneling through a square

In class we considered tunneling through a square potential barrier of height V0 and width a. In the solution to that problem we said the wave function inside the barrier was Psi_II(x)=Ce^(k2x)+De^(-k2x) For a barrier with V0 > E the first term in Psi_II(x) suggests a probability that increases with x which is counter intuitive.a) Assume C = 0 and determine the transmission coefficient T(C=0)=(A’/A)*(A’/A)=abs(A’)^2/abs(A)^2.b) If you did this correctly you will find T/T(C = 0) ≅ V0/4E using the form of T for V0 ≫ E given in class. The answer should have been T ≅ T(C = 0), a result only correct at V0 = 4E. This points out the fact that assumptions need to be carefully analyzed, even when they appear to be intuitively correct.

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