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

What makes expectation values real?

  1. Feb 7, 2015 #1
    If you have some wave function of some particle, say...

    |¥>

    And you calculate the expectation value of momentum, say...

    <¥|p|¥>

    What ensures that that spatial integral is real valued?

    Separately, all the components of the integral are complex valued
     
  2. jcsd
  3. Feb 7, 2015 #2

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    The operators, representing observables, are usually assumed to be self-adjoint, i.e., ##\hat{p}=\hat{p}^{\dagger}##. Now you have
    $$\langle \psi|\hat{p} \psi \rangle^*=\langle \psi|\hat{p}^{\dagger} \psi \rangle = \langle \psi|\hat{p} \psi \rangle,$$
    which implies that the expectation value is real.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What makes expectation values real?
  1. Expectation value (Replies: 5)

  2. Expectation Values (Replies: 1)

  3. Expectation value (Replies: 2)

  4. Expectation values (Replies: 1)

Loading...