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

Complex coefficents in density operator expansion?

  1. Dec 11, 2012 #1
    Hey, I recently had an exam where the quantum state were on the form

    [tex] |\psi\rangle = \frac{1}{\sqrt{2}} ( |+\rangle + i |-\rangle )[/tex]

    Here I formed the density operator for the pure state

    [tex] \rho(t) = |\psi\rangle \langle \psi| = \frac{1}{2} ( |+\rangle + i |-\rangle )( \langle +| - i \langle -| ) = \frac{1}{2} ( |+\rangle \langle + | + |- \rangle \langle - | + i(|-\rangle \langle + | - |+\rangle \langle -|)). [/tex]

    However in the solutions for the exam the complex i's were not there, i.e the solutions states that

    [tex] \rho = \frac{1}{2} ( |+\rangle \langle + | + |- \rangle \langle - | + |-\rangle \langle +| - |+\rangle \langle - |).[/tex]

    Have I missed something here or is the suggested solution erroneous? Is there a reason why a density operator expansion should not have complex coefficients?
     
    Last edited: Dec 11, 2012
  2. jcsd
  3. Dec 11, 2012 #2

    Jano L.

    User Avatar
    Gold Member

    Your solution seems correct - I've got i's on anti-diagonal as well. The second expression cannot be right, because the density matrix has to be hermitian.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex coefficents in density operator expansion?
  1. Density operator (Replies: 3)

  2. Density Operators (Replies: 27)

  3. Current density operator (Replies: 17)

Loading...