# Spin-one-half particle

## 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...

## The Attempt at a Solution

Related Advanced Physics Homework Help News on Phys.org
any insights?

Galileo
Homework Helper
Do you know the method for finding the eigenvalues and eigenvectors of an arbitrary matrix?

I guess not... :(

malawi_glenn
Homework Helper
I guess not... :(
that method is introduced in introductory Linear Algebra courses, so it is very strange that you have Quantum mechanics before having enough math knowledge. But you learn it easy, just get a book from your library and study.

nrqed