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I am confused with a line of text I read - it is an example of a 2D Hilbert space with orthonormal basis e1, e2. The Hamiltonian of the system is the Pauli matrix in the y-direction. Given by the matrix:

[tex]\sigma_{y} = (\frac{0, -i}{i, 0})[/tex]

The eigenvectors of the Hamiltonian are given by:

[tex]| \pm >_{y}= \frac{1}{\sqrt{2}}(| e_{1} > \pm i|e_{2}>)[/tex]

So, applying the time evolution operator to the eigenvectors gives:

[tex]U| \pm >_{y}=exp(\frac{-i(t-t_{0}) \sigma_{y}}{\hbar})| \pm >_{y}[/tex]

[tex]U| \pm >_{y}=exp(\frac{\mp i(t-t_{0})}{\hbar})| \pm >_{y}[/tex]

I don't understand how the last line came about?

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# Using the time evolution operator

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