- #1
omoplata
- 327
- 2
The following is from 'Modern Quantum Mechanics' by J.J. Sakurai, page 159.
[tex] \left( \frac{ \hbar }{ 2 } \right) \exp \left( \frac{i S_{z} \phi}{\hbar} \right) \left{ left( \mid + \rangle \langle - \mid \right) + \left( \mid - \rangle \langle + \mid \right) right} \exp \left( \frac{- i S_{z} \phi}{\hbar} [/tex]
[tex] = \left( \frac{\hbar}{2} \right) \left( e^{i \phi / 2} \mid + \rangle \langle - \mid e^{i \phi / 2} + e^{- i \phi / 2} \mid - \rangle \langle + \mid e^{- i \phi / 2} \right) [/tex]
How do I get from the first to the second?
[tex] \left( \frac{ \hbar }{ 2 } \right) \exp \left( \frac{i S_{z} \phi}{\hbar} \right) \left{ left( \mid + \rangle \langle - \mid \right) + \left( \mid - \rangle \langle + \mid \right) right} \exp \left( \frac{- i S_{z} \phi}{\hbar} [/tex]
[tex] = \left( \frac{\hbar}{2} \right) \left( e^{i \phi / 2} \mid + \rangle \langle - \mid e^{i \phi / 2} + e^{- i \phi / 2} \mid - \rangle \langle + \mid e^{- i \phi / 2} \right) [/tex]
How do I get from the first to the second?
Last edited: