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

[tex]E>V_1 & V_2[/tex]

So it's a step potential wave, setup. Let's set it up along the x axis. At x=0, there is the first step where it is [tex]V_1[/tex]. At x=a, there is another step, where [tex]V_2>V_1[/tex]. Show that the transmission coefficient is...

[tex]T=\frac{4k_1k_2^{2}k_3}{k_2^{2}(k_1+k_2)^{2}+(k_3^{2}-k_2^{2})(k_1^{2}-k_2^{2})sin^{2}k_2a}[/tex]

2. Relevant equations

So the usual transmission is just [tex]T=(\frac{A}{F})^{2}[/tex] where A is the coefficient for incoming wave, and F is coefficient for leaving wave. However, one of my friend says that the transmission coefficient has extra terms in it because the velocity of the wave is different. Please help!

3. The attempt at a solution

I have the eigenfunctions..

[tex]\varphi_1 = Ae^{ik_1x} + Be^{-ik_1x} [/tex]

[tex]k_1 = \sqrt{\frac{2mE}{h}}[/tex]

[tex]\varphi_2 = Ce^{ik_2x} + De^{-ik_2x}[/tex]

[tex]k_2 = \sqrt{\frac{2m(E-V_1)}{h}}[/tex]

[tex]\varphi_3 = Fe^{ik_3x} [/tex]

[tex]k_3 = \sqrt{\frac{2m(E-V_2)}{h}}[/tex]

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# Transmission Coefficient for two step potential

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