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Particle interchange and z component of spin 
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#1
Jun611, 10:34 AM

P: 842

The one thing that is NOT identical for different particles in a state is the z component of spin, having a probability of being positive or negative.
So when interchanging particles how do you handle the z component of the spin, it simply can't be interchanged along with the position and total spin as you could end up with a different state. 


#2
Jun611, 10:49 AM

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P: 1,266

If it is [tex]\uparrow\downarrow[/tex], you do get a different state.
Symmetric and antisymmetric combinations are eigenstates of total spin. 


#3
Jun611, 11:44 AM

P: 842

So how can the original hypothesis hold. What happens to the z component of spin, it must be transfered to the swapped particle. 


#4
Jun611, 07:19 PM

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P: 1,266

Particle interchange and z component of spin
When interchanging particles, all properties are interchanged. 


#5
Jun611, 07:30 PM

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[EDIT] that is a very simple example of how the Pauli exclusion principle is applied, and also why it is required. 


#6
Jun611, 07:39 PM

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#7
Jun711, 11:07 AM

P: 842

Oh I do see here that not all states satisfy the interchange hypothesis. Only combinations of states. I still do not see how this just makes it OK to swap particles when there is some probability that they have different spin up/down states, physically it is not logical.



#8
Jun711, 11:43 AM

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#9
Jun711, 11:58 AM

P: 842

An equal mix of up/down states for a large number of particles may work well. What happens when you only have two particles that are involved in the wave function? 


#10
Jun711, 12:04 PM

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#11
Jun711, 12:06 PM

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#12
Jun711, 12:19 PM

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For that example, they *will* have opposite spins when measured ... what does that have to do with anything? Once you measure the state, you "collapse" the wavefunction, so only one of the two possible components of the superposition can be observed. That is why we describe fermions in states like the one I gave as "spinentangled". 


#13
Jun711, 01:05 PM

P: 842




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