A particle with spin 1/2 in a potential well

[kisdrA]

Hello everyone. Help me solve the problem. I don't understand how to handle this type of task.

Find the energy levels of a spin 1/2 particle in a potential well: V(r)+W(r)*(l,s), where V(r<a)=-U, V(r>a)=0, W(r) = q*δ(r-a)

 

[PeterDonis]

Moderator's note: Thread moved to advanced physics homework help.

@kisdrA you will need to post any relevant equations and show your attempt at a solution.

 

[kisdrA]

 

[kisdrA]

It is clear that the problem in the potential $V(r)+W(r)*(l,s)$, but without the (l,s) term: $V(r)+W(r)$, simply reduces to solving the radial Schrodinger equation. And I understand how to find energy levels in such a task. But what to do when ls interaction also appears in the delta layer?