What I am interested in doing, is considering the angular momentum eigenstate for a spin ##1## system: ##|J=1, M=1\rangle = \begin{bmatrix}(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Overlap of coherent states

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Overlap coherent states | Date |
---|---|

I Two coherent sources | Sunday at 10:20 PM |

I Electron wavefunction as an overlap of orbitals | Jun 4, 2017 |

I Inequality for the time evolution of an overlap | May 20, 2017 |

A Overlap between ground states | Dec 10, 2016 |

I Identical particles distinguished by their trajectory? | Apr 18, 2016 |

**Physics Forums - The Fusion of Science and Community**