$\vec J=(J_x,J_y,J_z)$ 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.

  • $\begingroup$ Have you tried using Taylor expansion and the commutation relations? Please show how you have approached this problem. $\endgroup$
    – Roger V.
    Jan 18, 2023 at 13:41