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Homework Help: Square Potential Wells?

  1. Feb 2, 2010 #1
    Square Potential Wells???

    1. The problem statement, all variables and given/known data

    An electron is moving past a square well with energy [tex] E=3U_{0} [/tex]. What is the ratio of the de Broglie wavelength of the electron in the region x>L to the wavelength for 0<x<L?


    2. Relevant equations
    none that I can think of


    3. The attempt at a solution
    I know that for states of E greater than [tex] U_{0} [/tex] the particle is not bound but free to move through all values of x. The free particle wave functions are sinusoidal both inside and outside the well. I think the wavelength should be shorter inside the well than outside because of greater kinetic energy than outside. But how do i prove this???
     
  2. jcsd
  3. Feb 2, 2010 #2

    vela

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    Re: Square Potential Wells???

    How is the particle's energy related to its momentum, and how is its momentum related to its wavelength?
     
  4. Feb 2, 2010 #3

    Matterwave

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    Re: Square Potential Wells???

    I suppose, for the de Broglie wavelength, all you need to know is the momentum p. Classically, E (Kinetic) = p^2/2m. Can you go from there?
     
  5. Feb 2, 2010 #4
    Re: Square Potential Wells???

    Hi thx for the reply,
    I understand that E= p^2/2m and then how to find wavelength from there. So that equation is for the kinetic energy outside the potential well for free particle where E=3Uo but what is the energy state inside the well? and why is it greater?
     
  6. Feb 2, 2010 #5

    vela

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    Re: Square Potential Wells???

    Energy is conserved. Outside the well, it has K=3U0 and U=0. Inside the well, U=-U0, so how much kinetic energy must it have?
     
  7. Feb 2, 2010 #6
    Re: Square Potential Wells???

    oh I think I get it, so inside the well since U=-Uo then K=4Uo so energy is conserved! Thanks alot Vela appreciate it
     
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