- #1

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## Homework Statement

Find expectation values ##\langle \hat{S}_x \rangle##, ##\langle \hat{S}_y \rangle##, ##\langle \hat{S}_z \rangle## in state

##|\psi \rangle =\frac{1}{\sqrt{2}}(|+\rangle +|- \rangle)##

##|+\rangle## and ##|-\rangle## are normalized eigen vectors of ##z## projection of spin.

## Homework Equations

## \hat{S}_x=\frac{\hbar}{2}\sigma_x ##

## \hat{S}_y=\frac{\hbar}{2}\sigma_y ##

## \hat{S}_z=\frac{\hbar}{2}\sigma_z ##

where sigmas are Pauli matrices.

## The Attempt at a Solution

After calculation I get ##\langle \hat{S}_x \rangle=\frac{\hbar}{2}##, ##\langle \hat{S}_y \rangle=0##, ##\langle \hat{S}_z \rangle=0##

Why ##\langle \hat{S}_x \rangle## isn't zero if wave function is superposition of up and down in z-direction? Tnx for the answer!