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Homework Help: Schrödinger eq. with 3D spherical potential

  1. Apr 22, 2007 #1
    Hello!

    I'm trying to solve some old exam exercises to prepare for my qm exam next week.
    Now I got a question I dont have any idea how to solve it. I hope somebody can help me:

    "The radial Schrödinger equation in the case of a 3D spherical symmetric potential V(r) can be written in the form

    -h^2/(2*m) * d^2u/dr^2 + [V(r) + (l*(l+1) / r^2)]*u = E*u

    where u(r) = r*R(r). If V is attractive and vanishes exponentially at infinity, how does u(r) behave asymptotically for bound states?"



    Thanks for helping!
     
  2. jcsd
  3. Apr 23, 2007 #2
    What can you say about the effective potential as [tex]r\rightarrow \infty[/tex]? That should give you a pretty good idea of where to start. Also, I think this belongs in Homework Help.
     
  4. Apr 24, 2007 #3
    as r-> inf, the potential goes to zero and the second term in the effective potential goes rapidly to zero (as there is a r^2)
     
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