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Transmisson and Reflection (Quantum)

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  1. Oct 21, 2014 #1
    1. The problem statement, all variables and given/known data
    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)


    2. Relevant 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)

    3. 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.
     
  2. jcsd
  3. Oct 22, 2014 #2

    vela

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    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.
     
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