Consider the eigenvectors ##(0, 1)## and ##(1, 0)## for the quantum system described the magnetic field ##\vec{B} = (0,0,B)##.(adsbygoogle = window.adsbygoogle || []).push({});

Say I now rotate the magnetic field as ##\vec{B} = (B\sin\theta\cos\phi,B\sin\theta\sin\phi,B\cos\theta)##.

Then the eigenvectors are supposed to change as ##(\cos(\theta/2),e^{i\phi}\sin(\theta/2))## and ##(-\sin(\theta/2),e^{i\phi}\cos(\theta/2))##.

How can I prove that under SO(3) rotation, this is how the eigenvectors change?

P.S. : I've written the eigenvectors as row vectors, but they should be column vectors.

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# I SO(3) rotation of eigenvectors

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