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Unit vectors for multiple particles? (Quantum Mechanics)

  1. Sep 14, 2015 #1
    It's been a little bit since I have studied multi-particle quantum mechanics and I am a little rusty on the notation.

    Let's say I have a wave function, that consists of the tensor product of two spaces, one for each particle moving, ##|\psi_1,\psi_2>##. Each of these particles is moving in a certain direction defined by their respective unit vectors ##\hat{r}_n##, where ##n=1,2##.

    If I were to project this wave function onto the position basis to obtain it's functional form, how would I write the unit vectors? Would the unit vectors also have to be a tensor product? For example,

    [tex]<\vec{r}_1,\vec{r}_2|\psi_1,\psi_2>=f(\vec{r}_1,\vec{r}_2)\hat{r}_1 \otimes \hat{r}_2[/tex]

    Would this be correct??
     
  2. jcsd
  3. Sep 14, 2015 #2
    No, it's just an amplitude (complex number)
    [tex]<\vec{r}_1,\vec{r}_2|\psi_1,\psi_2>=f(\vec{r}_1,\vec{r}_2) \in \mathbb{Z}[/tex]
     
    Last edited: Sep 14, 2015
  4. Sep 14, 2015 #3
    Oh! Of course! Thanks!
     
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