 Solution

ID: past-exam-of-the-theoretical-physics-ii-course-of-the-university-of-cambridge/2012/paper-1/6/c/solution

At a finite potential step, both

u

and

u^{'}

are continuous:

A sin (k^{'} a) = B sin (ka + δ_{0}), A k^{'} cos (k^{'} a) = B k cos (ka + δ_{0}) .

k^{'} a cot (k^{'} a) = ka cot (ka + δ_{0}) .

At a zero of a denominator, the original two matching equations provide the continuous limiting condition.

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