Spin 1/2 system . in Sakurai quantum mechanics

1. Nov 27, 2015

1. The problem statement, all variables and given/known data

2. Relevant equations

This is a passage from Modern Quantum Mechanics by Sakurai ( page 26~27)

3. The attempt at a solution

I wonder how i can get 1.4.8 , 1.4.9 equations . and what do they mean?

2. Nov 27, 2015

blue_leaf77

They follow from the immediately preceding paragraph. It's mentioned that the probability for a measurement on the $z$ spin from a $|S_x;+\rangle$ state is equal to 1/2 for both up and down $z$ spin. This means the magnitude of the projections from the state $|S_x;+\rangle$ to the eigenstates of $z$ spin, $|+\rangle$ and $|-\rangle$, must be equal to $1/\sqrt{2}$.

3. Nov 28, 2015