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Radial function in Spherical potential well

  1. Nov 10, 2008 #1
    1. The problem statement, all variables and given/known data

    A Spherical potential which is
    0 for 0<r<a
    Vo for r>a

    Find the condition for bound states, for the radial function with l=0
    Plot the result.

    3. The attempt at a solution

    I have gotten the equation

    - tan(ka)=k/lambda
    where k is the wavenumber for the wave inside the well and lambda is the wavenumber for the wave outside the wave.
    I know these kind of equation have to be solved graphically or numerically. I have a similiar equation solved graphically in my textbook but I dont understand it. Can anyone please help me and give me a hint to how to solve this transcendental equation?
  2. jcsd
  3. Nov 10, 2008 #2


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    You just have to plot the two equations tan(ka) and k/lambda in a single graph. The intersection point between the function tan(ka) and the straight line k/lambda is the answer you need.
  4. Nov 10, 2008 #3


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    Science Advisor

    Except it's not a straight line, because lambda depends on k.
  5. Nov 10, 2008 #4


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    I see. Thanks, Avodyne.

    Then you have to plot of the graph of tan(ka) and k/lambda=k^2/2pi.
  6. Nov 12, 2008 #5
    I see. Thanks
    Last edited: Nov 12, 2008
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