- #1
sachi
- 75
- 1
We have a 1-d potential barrier,
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
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