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A Overlap of coherent states

  1. Jun 24, 2017 #1
    What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix}
    1 \\
    0 \\
    0
    \end{bmatrix}##, forming the coherent state ##|CS \rangle = \begin{bmatrix}
    0.5 \\
    -\frac{i}{\sqrt{2}} \\
    -0.5
    \end{bmatrix}## by taking the rotation ##\text{exp}(-\frac{i \pi}{2}\hat{J}_x)\begin{bmatrix}
    1 \\
    0 \\
    0
    \end{bmatrix} = \begin{bmatrix}
    0.5 \\
    -\frac{i}{\sqrt{2}} \\
    -0.5
    \end{bmatrix}##.

    I then want to work out the modulus squared of the overlap of the coherent state with a rotation of the coherent state about the ##x##-axis and the ##z##-axis for various values of ##\theta## and ##\phi##: $$|\langle CS| \text{exp}(-i \phi \hat{J}_z) \text{exp}(-i \theta \hat{J}_x)|CS\rangle|^2.$$ The result I get is this plot. Is this the type of plot you would have predicted? I would have expected something more circular symmetric?
    Thanks for any assistance.
     
  2. jcsd
  3. Jun 24, 2017 #2
    Looks quite circular symmetric to me, given that the origin is not in the middle of the figure.
     
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