Schrödinger eq. with 3D spherical potential

[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 don't 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!

 

[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.

 

[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)