1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Potential value , Bound state

  1. Nov 27, 2013 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m has a potential
    V(r)= -Vo r<a
    0 r>a

    Find the minimum value of Vo for which there's a bound state of energy and angular momentum are zero by solving shrodinger equation for E<0 and taking the limit E-> 0

    2. Relevant equations

    3. The attempt at a solution
    I want to know what does l represent in the radial shrodinger equation ? Is it the angular momentum ?
    For now, I considered l=0 and solved Shrodinger equation
    I got
    u(r)=C*sin(βr) with β=sqrt(2m(Vo+E)/h²)
    u(r)=Bexp(-kr) with k= sqrt(-2mE/h²)

    With boundary conditions we have

    Where am I supposed to use E->0 ..?
    Is it just in β=sqrt(2m(Vo+E)/h²)
    so that Vo=β²h²/2m ?
    Last edited: Nov 27, 2013
  2. jcsd
  3. Nov 28, 2013 #2


    User Avatar
    Homework Helper
    Gold Member

    You need to let E → 0 in both β and k.
  4. Nov 28, 2013 #3
    So we have that k=0 and then ? I dont Know what i have to do then
  5. Nov 28, 2013 #4


    User Avatar
    Homework Helper
    Gold Member

    What is the limit of β/k as E → 0? What does that tell you about the quantity βa in tan(βa)?
  6. Nov 28, 2013 #5
    We have tan(aβ)= -β/k=-sqrt(-1-Vo/E)
    so when E-> 0-
    so βa=-pi/2 ?
    Last edited: Nov 28, 2013
  7. Nov 28, 2013 #6


    User Avatar
    Homework Helper
    Gold Member

    Yes, except for the sign. β is a positive quantity.
  8. Nov 28, 2013 #7
    OK Thank you !
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Potential value , Bound state
  1. Bound states. (Replies: 1)