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Identical particles

  1. Oct 21, 2011 #1
    Hey I'm tring to grasp the symmetrization principle for identical particles. If the particles are indistinguishble, for example two electrons (not regarding spin), then [tex]\psi(x_1,x_2)[/tex] must correspond to the same physical situation as [tex]\psi(x_2,x_1)[/tex]. It follows that

    [tex]|\psi(x_1,x_2)|^2 = |\psi(x_2,x_1)|^2[/tex]

    and from this the symmetrization priciple follows as

    [tex] \psi(x_1,x_2) = \pm \psi(x_2,x_1)[/tex].

    This is all okay... However, if we had two electrons 1 and 2 with differents spins along the z-axis m1 and m2. Then how could the physical situation of 1 being at x1 with z-spin m1 and 2 being at x2 with spin m2 be the same as the situation of 2 being at x1 with spin m2 while 1 is at x2 with spin m1?

    That is how could the physical situation of

    [tex]\psi_{m_1,m_2}(x_1,x_2)[/tex]
    be the same as the situation

    [tex]\psi_{m_2,m_1}(x_2,x_1)?[/tex]

    Could'nt we just mesure the z-spin of the particle at x1 in the two situations and determine the difference?
     
  2. jcsd
  3. Oct 21, 2011 #2

    Bill_K

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    Science Advisor

    It's more like this... ψ(x1,m1; x2,m2) = -ψ(x2,m2; x1,m1). In both cases the electron at x1 has spin m1, and the electron at x2 has spin m2. What is being interchanged is the identity of the particles.
     
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