1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quantum operator hermiticity. Show that S is Hermitian

  1. Apr 30, 2014 #1
    1. The problem statement, all variables and given/known data
    Spin Operator S has eigenvectors |R> and |L>,
    S|R> = |R>
    S|L> =-|L>

    eigenvectors are orthonormal

    2. Relevant equations
    Operator A is Hermitian if <ψ|A|Θ> = <Θ|A|ψ>*



    3. The attempt at a solution
    <ψ|S|L> = <L|S|ψ>* // Has to be true if S is Hermitian
    LHS: <ψ|S|L> = <ψ|-|L>
    <ψ|-|L>* = <L|-|ψ>

    Question: how do i know how S acts on any function like |ψ> ?
    Could somebody provide an algorithm to find if an operator is Hermitian.
    I have another example of operator P, where P|R> = |L>
    P|L> = |R>
    How should i go on about this?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 30, 2014 #2
    Use the definition of a hermitian operator:

    [tex]\langle\psi|S|\psi\rangle^{\dagger} = \langle\psi|S^{*}|\psi\rangle = \langle\psi|S|\psi\rangle[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted