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Angular Momentum Eigenstate

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    The square angular momentum L2 and the z-component Lz of a free particle are measured. They are found to be L2=6[itex]\hbar^2[/itex] and Lz=[itex]\hbar[/itex]

    What is the state |l,m> of the system after measurement?

    2. Relevant equations

    L2|l,m>=[itex]\hbar^2[/itex]l|l,m>
    Lz|l,m>=[itex]\hbar[/itex]m|l,m>

    3. The attempt at a solution

    Is this simply:

    L2|lm>=[itex]\hbar^2[/itex]l|l,m>=6[itex]\hbar^2[/itex]|6,m>
    Lz|l,m>=[itex]\hbar[/itex]m|l,m>=[itex]\hbar[/itex]|l,1>

    |l,m> = |6,1> ?
     
  2. jcsd
  3. Oct 18, 2011 #2
    I'm getting some contradiction from my notes, the other way I see it the eigenstates could be |2,1>.
     
  4. Oct 18, 2011 #3

    vela

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    It's [itex]\vert 2 ~ 1 \rangle[/itex]. Your first "relevant equation" is incorrect.
     
  5. Oct 18, 2011 #4
    Cool, means page two of my notes needs a quick correction. Thanks!
     
  6. Oct 18, 2011 #5
    As a follow up to see if I'm slowly catching on; would the expectation value for Lx then be given by <lm|Lx|lm>?
     
  7. Oct 18, 2011 #6

    vela

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    Yes.
     
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