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Systems with more than 1 wave function

  1. Dec 11, 2014 #1
    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. jcsd
  3. Dec 11, 2014 #2


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    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 [itex] \hat x, \hat y[/itex] and [itex]\hat z [/itex].
  4. Dec 11, 2014 #3


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    Science Advisor
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    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
  5. Dec 11, 2014 #4
    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.
  6. Dec 11, 2014 #5


    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.

    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.

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