Transmisson and Reflection (Quantum)

[HelenaNikolai]

Homework Statement

Suppose a 12.0eV electrons approach a potential barrier of height 4.2eV.

For what barrier thickness is the reflection at a maximum?

Known:
v_0=6.7*10^(-19)J
E=1.9*10^(-18)J
m=9.11*10^(-31)kg
hbar=1.055*10^(-34)J*s
(I have converted from eV to J to make the units work)

Homework Equations

T=(1+(v_0)^2/(4E(E-V0))sin2(qL))^(-1)
q=sqrt(2m(E-v_0))/hbar
T+R=1
(Where T is the transmission probability and R is the Reflection)

The Attempt at a Solution

q=sqrt(2m(E-v_0))/hbar=sqrt(2(9.11*10^(-34))((1.9*10^(-18)-6.7*10^(-19)))/(1.055*10^(-34)

so then q=1.42*10^10
I plugged in q into my equation for T and then the v_0 and the E for the electron. I set all of it equal to zero, but I think that's my downfall. Conceptually T cannot be zero because L would have to reach infinity. I am not sure what is means by R being a maximum (aka L is a minimum) without setting T=0.

 

[vela]

T will not vanish even if L goes to infinity. This should make sense since the particle has more energy than the barrier height.

Try looking for when T is minimized, not 0.