Probability interpretation question

[arierreF]

If a have the following formula

ψ*(r1,...rn,σ1,...σn)ψ(r1,...rn,σ1,...σn)

how can interpret it?


the probability of finding a particle in a set of coordinates r1,...rn, with spin σ1,...σn or

the probability of finding a particle in a set of coordinates r1,...rn,σ1,...σn ?

I know that this is a stupid question...

 

[Jilang]

I would say the first. The second would make no sense from the notation.

 

[arierreF]

I googled it and i found that

ψ*(r1,...rn,σ1,...σn)ψ(r1,...rn,σ1,...σn) is the probability that the N particles are at a particular set of coordinates r1,...rn , with a particular spin σ1,...σn.

So we can not find the prob. for one particle? Just for the N particles?

 

[Jilang]

I guess that depends how many particles are in the system and whether they are entangled or not. If they are entangled you won't be able to separate the wave-function out for a single particle.

 

[arierreF]

Ok, but I am still not understanding something.

Considering that the N particle are entangled,

My thought:
probability that the N particles are at coordinates r1,...rn , with spin σ1,...σn.

Google answer:
probability that the N particles are at a particular set of coordinates r1,...rn , with a particular spin σ1,...σn.

what is the difference?

 

[Jilang]

I don't think there is any difference. Each n will refer to a different particle. Sorry if I am not understanding the confusion properly.

 

[arierreF]

Ok i got it.

Thanks for the help.