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

The interference term. Confused.

  1. Jun 27, 2011 #1
    Can someone explain what the difference is between the expectation value of an observable in a pure vs a mixed state. The equations are identical. For example with spin up and down [tex]|A|^2<S_u|O|S_u> + |B|^2<S_d|O|S_d>[/tex]
     
  2. jcsd
  3. Jun 27, 2011 #2

    Bill_K

    User Avatar
    Science Advisor

    What you've quoted is <O> for the case where the system is in an incoherent mixture of |Su> and |Sd>. This would be a classical mixture, like heads and tails on a coin, and is represented by a density matrix rather than a wavefunction.

    More typically what we mean by a mixed state is a coherent mixture, |S> = A |Su> + B |Sd>, in which case the expectation value <S|O|S> will need to include interference terms A*B <Su|O|Sd> and B*A <Sd|O|Su>.
     
  4. Jun 27, 2011 #3
    If you could quickly reference page 358 of this pdf http://www.physics.sfsu.edu/~greensit/book.pdf [Broken]

    It shows that your equation is equivalent to mine...
     
    Last edited by a moderator: May 5, 2017
  5. Jun 27, 2011 #4

    kith

    User Avatar
    Science Advisor

    That's true only if your states are eigenstates of O (so the interference terms vanish).

    This means, you can't distinguish between a coherent superposition and an incoherent mixture by measuring in one basis alone. But you don't get identical expectation values in all bases!

    Consider a superposition of 50:50 spin up and spin down along a given axis. If you change your measurement axis (corresponding to another basis) you get other ratios. In the case of incoherent mixing, the ratio is 50:50 regardless of basis. You can verify this by an easy calculation of the corresponding density matrices.
     
  6. Jun 27, 2011 #5
    What are the terms that vanish. If the system is mixed or pure it does not have any extra terms.

    Edit: I see the term now, I looked right over it, thanks!
     
    Last edited: Jun 27, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: The interference term. Confused.
Loading...