Yukawa Potential: Analyzing Shapes & Angular Momentum

[the keck]

Homework Statement

A particle moves under the Yukawa Potential of (-alpha)*exp(-kr)/r where k is real. Discuss all possible shapes of the effective potential. At what values of angular momentum L can the particle move in the potential with finite/bounded motion

The Attempt at a Solution

The first part, I can sort of do, but there's so many combination of shapes, since we are saying here alpha & k could be greater or less than zero or equal to zero. The second part concerning angular momentum I am totally at a loss

Thanks

Regards,
The Keck

 

[valtorEN]

just graph it and look! :)

 

[Meir Achuz]

Angular momentum gives a 1D potential L(L+1)/2mr^2.
For high enough L, the total potentiall will have no negative part.

 

[sp105]

I wish to have more information regarding how you come to calculate l(l+1)/2mr^2 as a angular momentum for yukawa potential