Transmission Through a Delta Function Potential
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 54
23-8-2016
1733
Transmission Through a Delta Function Potential
A particle of mass m moves in one dimension where the only potential V(x) = Cδ(x) is at the origin with C > 0. A free particle of wave vector k approaches the origin from the left. Derive an expression for the amplitude T of the transmitted wave as a function of k, C, m, and h.
SOLUTION
On the left the particle has an incident intensity, which we set equal to unity, and a reflected amplitude R. On the right the transmitted amplitude is denoted by T.
(1)
At the point x = 0, we match the value of ѱ(x) on both sides. We match the derivative according to an expression with C = C'. This yields two equations for T and R which can be solved for T:
(2)
(3)
(4)
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