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Homework Help: Expectation value in quantom mechanics (a general question)

  1. Nov 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Hello, I'm a bit confused about the calculation of the expectation values. Normally, when I have a wave function of sort and I want to calculate the expectation value of some operator, I just insert it into the braket <ψ|A|ψ>, where ψ for example is a wave function composed out of eigenstates ψ=1/√3⋅(φ123)
    and I will just multiply those accordingly.
    My problem started when I was asked to calculate uncertainty for Lx and Ly, I keep seeing the expectation value it's being calculated like this:
    Lx=1/2⋅<lm|L++L-|lm>=0, with both bra-ket are for the same state. I don't understand, why can't the wavefunction be one that is composed out of several different eigenstates?
    2. Relevant equations

    3. The attempt at a solution
    When I calculated it at first, I did:
    <Lx>=1/2⋅<lm|L++L-|l'm'>, which confused me even more, since this is actually a calculation for the Lx matrix elements. What am I doing wrong here?
  2. jcsd
  3. Nov 23, 2014 #2


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    So far I see nothing wrong.
    So what you see there is that they calculate Lx for a state |lm> that is an eigenstate of both L2 and Lz.
    Apparently you have a different state Ψ so you get something different. Where 's the contradiction you see ?
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