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Incompatible observables

  1. Jul 10, 2004 #1
    Incompatible observables do not share a complete set of common eigenfunctions, because their operators do not commute.

    It seems that, incompatible observables like x and p_x, S_x and S_y do not have any common eigenfunction at all.

    Can anyone give a concrete example of a pair of incompatble observables that have common eigenfunctions but incomplete (do not span the Hilbert Space)?
  2. jcsd
  3. Jul 10, 2004 #2

    Tom Mattson

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    The only example I can think of is the state of zero orbital angular momentum. The eigenfunction common to the incompatible operators Lx, Ly, and Lz is the spherical harmonic Y00, with a zero eigenvalue.
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