Homework Help: Schrödinger eq. with 3D spherical potential

1. Apr 22, 2007

maethros

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. Apr 23, 2007

StatMechGuy

What can you say about the effective potential as $$r\rightarrow \infty$$? That should give you a pretty good idea of where to start. Also, I think this belongs in Homework Help.

3. Apr 24, 2007

valtorEN

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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