Consider an electron with total energy E>V2 in a potential with V(x)={∞x<0V10<x<LV2x>L
We can determine that ϕE(x)={0x<0Asin(kx)+Bcos(kx)0<x<LCeqx+De−qxx>L
We can also apply the boundary condition at x=0 to determine that ϕe(x)=Asin(kx)
We can also apply boundary conditions at x=L to find that Asin(kL)=De−qL
I'm stuck with the question: are the energy states with E>V2 quantized?
I can see that, because the boundary condition at x=L is not homogeneous, we cannot determine the eigenvalues in discrete form. Does this mean that the energy states are not quantized in this case?
Would appreciate some help.
Answer
Asin(kiL)=De−qL
But particles with energy E>V2 can not be bound (contained in the well). Such a particle, coming in from the right e.g., would simply bounce off the infinite potential wall.
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