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I How do I find this state |j,m=j> to calculate another state?

  1. Aug 5, 2016 #1
    I’m confused about how you find the vector |s;s⟩ to use in the general equation
    |θ,ϕ⟩=exp(−iϕS3) * exp(−iθS2) |s;s⟩
    For spin Coherent states (From http://www.scholarpedia.org/article/Coherent_state_(Quantum_mechanics)#4._Spin_Coherent_States
    Eq 12)
    Or
    how you find the vector |j,m=j⟩ to use in the equation
    |θ,ϕ⟩=exp(iθ[Jx*sin(ϕ)−Jy*cos(ϕ)]) |j,m=j⟩
    (From https://arxiv.org/pdf/0805.1264v1.pdf
    Eq 14)

    For the above state |j,m=j⟩ in the paper it appears to be assumed you should just know how to find this. I know that it is an eigenstate but I don’t know how to go from there to get that vector so that I can solve for |θ,ϕ⟩
    I need it for j=4 but I’d like to be able to understand how to get it for any j and understand why?
     
  2. jcsd
  3. Aug 5, 2016 #2

    A. Neumaier

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    Science Advisor
    2016 Award

    As explained in your first link, ##|s,s\rangle## is the normalized eigenvector of ##S_3## to the eigenvalue ##s##. So you pick the representation you have, write down the operator ##S_3## in a basis of this representation, and find the eigenvector numerically.
     
  4. Aug 5, 2016 #3
    Thank you,
    Sorry I missed that, I've figured out what I need now thank you so much
     
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