Can Quantum Particles Meet Everywhere on the Diagonal?

[jk22]

Since particles have their own space i heard they cannot meet. But how about the origin if we see the axes perpendicular ?

 

[Jazzdude]

Hah, that's a good one! I hadn't heard that one before. If that was true you could make the same argument for classical particles. Their configuration space is also 3n dimensional and every particle "has its own space". Quantum theory just assigns an amplitude to every point in that same space. So nothing changes in terms of "meeting" and "own space".

 

[DrClaude]

Since particles have their own space i heard they cannot meet.

What space are you talking about? Real space? Hilbert space?

And what do you mean by "meet"? Does "interact" count?

 

[jk22]

I mean the configuration space. Meet would mean be at the same place.

1 dimensionally Classically we have x1,x2 in R and in quantum mechanics they "live" on two perpendicular axes in R2 so that classically if x1=x2 they are at the same place whereas not in quantum words (except 0) ?

 

[Demystifier]

If you think about particles as objects in the configuration space, them you don't really talk about two or more particles. One point in the configuration space (being it the origin or any other point) represents one (abstract) object. With one object only, the notion of "meeting" does not make sense. And that applies to both classical and quantum mechanics.

On the other hand, if you think of x1 and x2 as positions of two particles, than they meet each other everywhere on the diagonal x1=x2 through the origin, not only at the origin x1=0, x2=0.