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## Homework Statement

1. find eigenvalue of operator S_y for spin 1/2 particle

2. find eigenvector for the same S_y

3. Find average value that'll be obtained after numerous independent measurement of S_y if electron is in spin state |+>

## The Attempt at a Solution

1. the eigenvalue is just: S_y=(hbar/2)[matrix] where the matrix is:

[0 -i]

[i 0]

So S_y=-(hbar/2)?

How does the possibility of +(hbar/2) come in, mathematically..?

2. My book says that the eigenvector of S_y is:

|plus or minus> = (1/sqrt(2)) [ |+> plus or minus i|-> ]

I'm not really sure what to make of the notations.... :(

3. Since S_y=-(hbar/2) and

|+> = vertical maxtrix[cos(theta/2)]

[sin(theta/2)]

and

<+| = horizontal matrix [ cos(theta/2) sin(theta/2)]

<+|S_y|+> = -(hbar/2)sin(theta)

Is that correct...? Because it's the same value as the expectation value for S_x, right? I'm not really sure what I should be expecting for these values...