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

Probability Density or Expectation Value?

  1. Apr 16, 2010 #1


    User Avatar
    Gold Member

    In a paper in Physical Review A, the author discusses a wave function for one particle, Ψ(r,t), where r is the position vector.

    He writes "The probability distribution for one-particle detection at a point r is given by

    |<r|Ψ >|2 ".

    Is that correct? The above expression looks, to me, more like the expectation value for r.

    Shouldn't the probability distribution be |<Ψ|Ψ >|2?

    Thanks in advance.
  2. jcsd
  3. Apr 16, 2010 #2


    User Avatar
    Science Advisor

    No, that is correct. The position representation of the wavefunction is given by <r|Ψ > ... you can derive this from the resolution of the identity for the continuous distribution of eigenstates ... see the first chapter (I think) of Cohen-Tannoudji for a detailed derivation. Since <r|Ψ > is the wavefunction, then of course |<r|Ψ >|2 is the probability density.

    For a normalized wavefunction, <Ψ|Ψ >=1, so that certainly isn't correct.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook