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## Homework Statement

I have a two spin 1/2 particles. The Hamiltonian for the system is given as H = w

_{1}S

_{1z}+ w

_{2}S

_{2z}. I need to find the possible values and their probabilities when I measure S^2 at some later time T. Also the Initial state \Psi (0) = a | [tex]\uparrow[/tex] [tex]\downarrow[/tex] > + b | [tex]\downarrow[/tex] [tex]\uparrow[/tex]>

## Homework Equations

## The Attempt at a Solution

Now I know for a 2 spin 1/2 particle system, s = 1 and 0.

The eigenvalue equation for S

^{2}is S

^{2}|sm> = hbar

^{2}( s ( s+1) )|sm>

So the possible values are 2 \hbar^2 and 0.

I know at some later time, the state will look like \Psi(t) = a e

^{{-iE_1 t/ \hbar}}+ b e

^{{-iE_2 t/ \hbar}}

and I can find E_1 and E_2

However, how do i find the probabilities?

If I was just looking for S_z probabilities, I know it would be a

^{2}for spin up and b

^{2}for spin down. I also know that if I was looking for S_x I would need to evolve the coefficients in time. However, how do I measure the probabilities of S

^{2}?