# Systems with more than 1 wave function

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?

## Answers and Replies

ShayanJ
Gold Member
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 $\hat z$.

• ghost313
dextercioby
Science Advisor
Homework Helper
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:
• 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.

bhobba
Mentor
I red somewhere that there are quantum fields

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.

I don't know if that answers your query though because I cant follow your issue.

Regarding your original question your equation simply expresses the fact quantum states form a vector space - this is known as the principle of superposition.

Exactly what a quantum state is is a difficult issue being very interpretation dependant. If you want to pursue that best to start a new thread.

Thanks
Bill

• vanhees71 and ghost313