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Particle physics basic concept from Standford Uni help

  1. Feb 21, 2016 #1
    Let's start with a vacuum, I will write |0000......> as |0>.
    $$ \psi^+ (x) |0\rangle = \sum_k e^{-ikx} a^+ (k) |0\rangle $$

    Qns: What happens if you superpose/add up state vectors corresponding to a particle of momentum k and you add up with coefficient e-ikx?
    $$ \sum_k e^{-ikx} a^+ (k) |0\rangle $$ where a+ is a creation operator

    Ans: The ans is it is a position state. It is a state with a definite position. What is a position? x. If you add up momentum states with e-ikx, that gives you a position state located at particle x. This is one particle quantum mechanics.

    Source: Starts at 40:21

    I am lost at this part whereby how multiplying e-ikx with a+(k) gives the position state?
  2. jcsd
  3. Feb 21, 2016 #2


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    Gold Member

    You need to look at the Fourier expansion of a delta function which is the wave function for a particle localized at a point position.
    Any position vs momentum picture transformation is going to be a Fourier expansion of the other. Here you simply have it applied to operators in the field theory.
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