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Homework Help: Dirac bubble potential

  1. Nov 27, 2011 #1
    Dirac "bubble potential"

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

    Consider a radially symmetric delta potential V(r) = −Vo * δ(r − a) with l=0. How many bound states does this system admit?

    3. The attempt at a solution

    With l=0, the radial equation reduces to the one dimensional TISE. So, solving the 1D TISE with a delta potential V(r) = −Vo * δ(r − a):

    I have [tex]R_{in} = A\exp{kr}[/tex] for r < a
    [tex]R_{out} = A\exp{k(2a-r)}[/tex] for r > a

    which I obtained my matching the condition R_in = R_out at r=a. Also, the "discontinuity equation" gives me that

    [tex] k = \frac{mV_o}{\hbar^2} [/tex]

    meaning that there is only one energy and only one bound state. I don't believe this to be correct... especially since the question hints that the number of bound states should depend on "a".

    Any help please?
     
  2. jcsd
  3. Nov 29, 2011 #2
    Re: Dirac "bubble potential"

    Bump.
     
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