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The SE of a particle in a ring

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data

    Write down the Schrödinger equation for a particle inside a circle of radius R


    2. Relevant equations

    - Gradientψ(r,θ)=Eψ(r,θ)




    3. The attempt at a solution

    Take the gradient in spherical form and set r = R; θ=90;∅ as 0

    Then you are left with the first two terms of the gradient where sin(90) = 1 and r = R.

    I thought I was approaching this correctly but the solutions show this

    (d/dr)^2 + 1/r (d/dr) + 1/r^2 (d/dθ)^2

    I am not sure how are why you should get three three when the way I am thinking of it "phi" term will be zero.

    Thanks for any help in advance!

    Anand
     
  2. jcsd
  3. Oct 27, 2011 #2

    dextercioby

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    Homework Helper

    1. Do you know how the SE looks like in cartesian coordinates in a plane ? (2 dimensions)
    2. Can you use the symmetry of the problem to simplify the equation at 1. ?
     
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