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$\vec J=(J_x,J_y,J_z)$ is angular momentum and $\vec v$ is a vector.

I want to know how to compute the matrix element of $\exp(\vec v\cdot\vec J)$, namely $$ \langle jm\left|\exp(\vec v\cdot\vec J) \right|jm'\rangle $$ where $\left| jm \right.\rangle$ is the eigenstate of $\hat J_z$.

Further more, I want to know $$ \langle jm \left|\vec J\exp(\vec v\cdot\vec J) \right|jm'\rangle. $$

Thanks for answering.

John Rennie
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Luessiaw
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  • Have you tried using Taylor expansion and the commutation relations? Please show how you have approached this problem. – Roger V. Jan 18 '23 at 13:41

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