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Please help me with this question!

  1. Nov 21, 2007 #1
    1. The problem statement, all variables and given/known data

    An electron is in a 1 dimensional potential well. If the energy of the electron is < V0, show that the probability density P(x) for the electron falls exponentially:

    P(x) = Aexp(-x/L)


    I honestly have no clue, I've been trying all day to do this!
     
  2. jcsd
  3. Nov 21, 2007 #2

    berkeman

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    Staff: Mentor

    You need to show us what you have been doing "all day", so that we can help to guide you in the right direction. What is the basic equation that you should be using to approach this problem? It has a catchy name....
     
  4. Nov 21, 2007 #3
    [tex]\frac{-h bar^{2}}{2m}[/tex] [tex]\frac{d^2\psi}{dx^2}[/tex] = (E - V[tex]_{0}[/tex])[tex]\psi[/tex]

    So thats the schrodinger equation for when the energy is less than V0 I think...

    Then to show the probability density...

    P(x) = [tex]\int[/tex][tex]\psi[/tex](x)* [tex]\psi[/tex](x) = 1

    I have no idea what to do next...
     
  5. Nov 21, 2007 #4

    Dick

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    Ok, so the schrodinger equation is psi''=k*psi, where k is a positive constant. What do the solutions to that equation look like?
     
  6. Nov 22, 2007 #5
    The solutions are of the form

    [tex]\psi[/tex] = Ae[tex]^{ikx}[/tex] + Be[tex]^{-ikx}[/tex]
     
  7. Nov 23, 2007 #6

    Dick

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    Noooo. The k in psi''=k*psi is real and positive. How about A*exp(sqrt(k)*x)+B*exp(-sqrt(k)*x)?
     
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