Can someone please explain the following. I am mainly curious as to why sigma only appears in front of the sin. Thanks!

$$ exp(\frac{\pm i\vec{\sigma} \cdot \hat{n}\phi}{2}) = cos(\phi/2) \pm i\sigma_zsin(\phi/2) $$

Question

Can someone please explain the following. I am mainly curious as to why sigma only appears in front of the sin. Thanks!

$$ exp(\frac{\pm i\vec{\sigma} \cdot \hat{n}\phi}{2}) = cos(\phi/2) \pm i\sigma_zsin(\phi/2) $$

loser66 · Answer

woa it looks strange to me, question: which course this equation come from?

anonymous · Answer

This is from a quantum mechanicsbook but is an introduction chapter to get you used to work with vectors, matrixes, bra's and kets. (Modern quantum mechanics, J.J. Sakurai 1.3)

loser66 · Answer

physics?

anonymous · Answer

This is more of a math question than a physics question however.

dan815 · Answer

look up proof for eulers formula

dan815 · Answer

therse a nice khan academy video showing u the proof of eulers formula

dan815 · Answer

do u want link?

anonymous · Answer

I'll check it out. tried that myself but was getting a different answer last night.

dan815 · Answer

ok

anonymous · Answer

@dan815, thanks!. I didn't use series to show it before and it didn't occur to me that simga_z^2 = I.