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Homework Help: Obtaining the angular momentum state of two spin 1/2 particles for (S=0)

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data

    consider the possible angular momentum states |s,m>, of a system of two spin-1/2 particles

    construct all possible states with total spin zero (S=0)

    2. Relevant equations

    3. The attempt at a solution

    if total S of system is zero, m must also equal zero. So the only state is |s=0,m=0>

    and |s=0,m=0> = 1/sqrt(2)[ up*down - down*up ]

    I got the exact form of |0,0> from my text book, but I dont understand how this particular combination of up/down states is aquired.

    considering the state |s=1,m=1>, its intuitive that m can only equal 1 if both spins are +1/2. The same goes for |s=1,m=-1> where both spins are -1/2.

    Then one can obtain |s=1,m=0> by applying the lowering operator to yield:

    |s=1,m=0> = 1/sqrt(2)[up*down+down*up)

    my book gives a thorough explanation i deriving the s=1 states, but then it just gives the S=0 state without much explanation.

    so how do you obtain |s=0,m=0> = 1/sqrt(2)[ up*down - down*up ] ?
  2. jcsd
  3. Nov 29, 2012 #2


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    Welcome to PF!

    Can you show that the state |s = 0, m = 0> must be orthogonal to |s = 1, m = 0>?
    Last edited: Nov 29, 2012
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