Rectangular Potential Barrier Boundary Conditions with E=V

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SUMMARY

This discussion focuses on calculating the transmission and reflection coefficients for a rectangular finite potential barrier when the energy of the particle (E) equals the height of the barrier (V0). The participant expresses confusion regarding the boundary conditions and the treatment of the imaginary number in the exponential terms of the general solutions. The participant questions the accuracy of the Wikipedia page on rectangular potential barriers, specifically regarding the disappearance of the imaginary component in the Cl term. The discussion highlights the common practice of simplifying the barrier range from x=0 to x=a for easier application of boundary conditions.

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GoliathPSU
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Homework Statement


I am trying to calculate the transmission and reflection coefficients for rectangular finite potential barrier between (-a, a) for a particle of mass m with energy equal to the height of the barrier (E = V0 > 0).

Homework Equations


http://en.wikipedia.org/wiki/Rectangular_potential_barrier#E_.3D_V0

The Attempt at a Solution


I understand the general solutions for the potential region are linear, and am trying to match the boundary conditions to evaluate the coefficients, but I am having trouble understanding why the Wikipedia page linked above has the imaginary number disappear from the exponentials attached to the Cl term. Instead there is just a + sign there. Is this just a mistake on the page? As far as I can tell, there is no reason the term should suddenly become real.
 
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I agree with you. No one notices, because they let Cl=0 for T and R .

By the way, usually the barrier is from x=0 to x=a to make applying the boundary conditions a little easier.
 

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