We have a 1-d potential barrier,(adsbygoogle = window.adsbygoogle || []).push({});

V(x)=0 for x<0,x>a

V(x)=V1 for 0<=x<=a

we are considering the case where E>V1. we consider the case when transmission resonance occurs i.e when there is no reflected wave. this is when

[2m/(hbar^2) * (E-V1)]^0.5 = n*Pi/a

where n is an integer

we are then asked to describe what the wavefunction looks like in the region 0<=x<=a when transmission resonance occurs. we have already found the wavefunction in this region to be

psi = Aexp(Kx) + Bexp(-Kx)

where K = [2m/(hbar^2) * (V1-E)]^0.5

we know that K is imaginary as V1<E, which would suggest that we had sinusoidal wavefunctions. However, we also find that both A and B are themselves complex!! I'm very confused about this situation. I think we essentially have complex valued sinusoids in this region. any suggestions would be greatly appreciated.

Sachi

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# Homework Help: Transmission resonances, QM

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