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Homework Statement
Prove that ## e^{2\pi i \mathbf{n\cdot J}/\hbar} |j,m\rangle = (-1)^{2j}|j,m\rangle ##. This equation is from Ballentine's QM book. The term in front of the ket state in the LHS is a rotation operator through ##2\pi## angle about an arbitrary direction ##\mathbf{n}##.
Homework Equations
Above
The Attempt at a Solution
I can prove this for spin one half particle using the identity ## (\mathbf{ \sigma \cdot n})^2 = 1##, but not for an arbitrary j. Does he simply quote this from the result of E. P. Wigner's work, as also stated in the book?