# Systems with more than 1 wave function

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1. Dec 11, 2014

### ghost313

Hello,I am new to quantum mechanics.I just want to clear this equation:

ψ(x) = ∑n anψn(x)

What does this actually mean?Is this equation telling us that the system is moving as a wave?
Or,as I think,for example lets suppouse we have 2 electrons in a system,and the wave function becomes this ψ(x),does that mean that electrons interact one with the other?

2. Dec 11, 2014

### ShayanJ

That's not a physical statement but a mathematical one and only means that we're using some base functions to expand the wavefunction, like expanding a 3D vector in terms of $\hat x, \hat y$ and $\hat z$.

3. Dec 11, 2014

### dextercioby

No, actually multiparticle systems use the concept of tensor product of uniparticle spaces. So the product, not the sum appears in the formula of a general state.

Last edited: Dec 11, 2014
4. Dec 11, 2014

### ghost313

I red somewhere that there are quantum fields which imply that one wave function(1 electron) can intercept on another wave functions (1 or more electrons),and so reverse...eaven when r → ∞ r(distance) so their Potential Energy(V) V → 0.
What does that mean then?
Thank you btw for answearing.

5. Dec 11, 2014

### Staff: Mentor

In Quantum Field Theory you don't have one particle. All the electrons in the universe are described by excitations in the same underlying field.