(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]>

2. Relevant equations

3. 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}?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Possible values and their Probability of Measuring S^2 - Spin

**Physics Forums | Science Articles, Homework Help, Discussion**