(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A beam of particles, each of mass m and kinetic energy E, is incident on a potential barrier

[tex] V(x) = V_0 \; \; for \; \; 0 \leq x \leq a [/tex]

[tex] \; \; \; \; \; \; \; \; \; = 0 \; \; for \; \; x < 0 \; \; and \; \; x > a [/tex]

[tex] E = V_0 \; \mbox{is the special case}[/tex]

The part of the problem i'm on is finding the transmission probability

3. The attempt at a solution

I've solved the Schrodinger Equation and equated the solutions at the two boundaries which gave me

[tex] C + D = B [/tex]

[tex] ik(C - D) = A [/tex]

[tex] Aa + B = Ge^{ika} [/tex]

[tex] A = kiGe^{ika} [/tex]

[tex] A, B, C, D, G \; \mbox{constants}[/tex]

I feel like im just going round in circles finding the transmission probability, in my notes I have transmission prob as [tex] (\frac{G}{A})^2 [/tex]. However, a hint at the bottom says once the 4 continuity equations have been found, eliminate A and B, which I've tried and doesn't seem to get me any where!

If anyone has some advice or could push me in the right direction that would be really appreciated. Thanks

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# Potential Barrier - Special Case!

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