What do these states mean physically?

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KFC

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For the state written as

[tex]|u, d\rangle[/tex]

where u mean spin-up and d mean spin-down, I know that it is a state for a system which contains two spins: the first one is up and the other is down.

But if I write the state as

[tex]|u\rangle + |d\rangle[/tex]

What does this state mean? To me, I will read there are two partilces: one spin up and one spin down, so what's the different from the first one?

It is more confuse if I write the Fock states

what does [tex]|4, 3\rangle[/tex] mean ? The first subsystem has 4 particles while the other has 3 particles?

And [tex]|4\rangle + |3\rangle[/tex] ?
 
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|u>+|d> is a system with only one spin, in a (non-normalised) superposition of both up and down. Note the difference between the (vector) addition operator and the tensor product operator (which is what you are abbreviating when you use the notation of a comma inside one ket).

..this "superposition" state does have a specific "phase", so it is different from another single-spin state |u>-|d>, in fact pure up (say) can also be written as a particular superposition of those two different "phase" states..
 
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