Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Electron spin and the Pauli Exclusion Principle.

  1. May 16, 2012 #1
    How is it that only 1 spin up and 1 spin down electron are allowed in an atom even though there is no measurement to collapse the state function?
  2. jcsd
  3. May 17, 2012 #2


    User Avatar
    Science Advisor

    That is not the case.

    You typically chose a basis in a Hilbert space. One possibility is |+1/2> and |-1/2> w.r.t. to the z-direction; but all other directions are allowed as well to define a basis.

    In addition in an atom with more than one electron (like HeĀ² with total spin S=0) it is not true that the "first electron has spin +1/2" and the "second one has spin -1/2" w.r.t. to z. Instead the two electrons are in an entangled state. An ansatz taking antisymmetrization into account is the Slater determinant.

    Of course one may chose the z-direction to define the basis; but the state is independent from this choice.
  4. May 17, 2012 #3
    Then how does the third electron 'know' that it can't have spin n,l,m.s = 1,0,0,+1/2 (s w.r.t z)? As you just said yourself, this state is unoccupied.
  5. May 17, 2012 #4


    User Avatar
    Science Advisor

    I am only saying that you cannot distinguish between "the first" and "the second" electron. And you should not say that "one electron has spin +1/2 w.r.t. z" whereas "the other one has spin -1/2 w.r.t. z"; that's not wrong but misleading. Both spins couple to S=0. You don't have to mention the z-axis in order to specify the singulet state S=0.

    The two states

    [tex]|1s,\uparrow_z\rangle|1s,\downarrow_z\rangle - |1s,\downarrow_z\rangle|1s,\uparrow_z\rangle[/tex]


    [tex]|1s,\uparrow_x\rangle|1s,\downarrow_x\rangle - |1s,\downarrow_x\rangle|1s,\uparrow_x\rangle[/tex]

    are identical w.r.t. to total spin S.
    Last edited: May 18, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook