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Incompatible observables

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Say I have two incompatible observables A and B. A has a finite number of base states say 4. How many base states should B have?

    2. Relevant equations

    Heisenberg's uncertainty

    AB - BA <> 0

    3. The attempt at a solution

    I guess the answer is 4 as A and B basis states should form basis in the same space, but not very sure.
     
  2. jcsd
  3. Nov 11, 2012 #2

    mfb

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    Staff: Mentor

    I agree with that.
     
  4. Nov 11, 2012 #3
    have a second thought. If A's states are (1), (2), (3), (4), can't B states be a subspace of that basis, such as (1') = 1/sqrt(2) [(1) + (2)]; (2') = 1/sqrt(2) [(1)- (2)], no contribution from (3) and (4)?
     
  5. Nov 11, 2012 #4

    mfb

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    State 3 and 4 need some representation in B, too.
    (1',2') can be rotated (1,2).
     
  6. Nov 11, 2012 #5
    You are right, thanks
     
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