Spin 1/2 systemin Sakurai quantum mechanics

[BREAD]

Homework Statement

Homework Equations

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

The Attempt at a Solution

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

 

[blue_leaf77]

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

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 $1/\sqrt{2}$.

 

[BREAD]

Then what is e^i*delta

 

[blue_leaf77]

The expansion coefficient is in general complex, and that complex exponential is set there to account for this fact, neglecting the overall phase factor as this is not influential for a measurement.