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Basic Quantum Tunneling question

  1. Nov 18, 2013 #1
    1. The problem statement, all variables and given/known data
    A particle of energy E approaches a step barrier of height U. What should be the ratio E/U be so that the reflection coefficient is 1/2.


    2. Relevant equations
    Transmission + Reflection = 1
    Transmission = e^(-2a*alpha)
    a = mw∏/h
    alpha^2 = (8m∏^2/h^2)(U-E)

    Reflection = (k1-k2)^2 / (k1+k2)^2



    3. The attempt at a solution
    So this is a little bit messy.. I assume most people that are going to help me are familiar with these basic transmission and reflection equations. Anyway is there a possible way to solve this problem an get a ratio that is JUST a number? wouldn't you always have other variables in it since it's talking about a completely undefined particle? there are no ways to get the m's and w's out of the equations right?
     
  2. jcsd
  3. Nov 18, 2013 #2

    Simon Bridge

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    All those k's depend on energy.
    Expand them out in the reflection coefficient and see what happens.
     
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