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Quantum mechanics , total orbital angular momentum?

  1. Jan 1, 2014 #1
    1. The problem statement, all variables and given/known data

    A hydrogen atom is identified as being in a state with n=4. What is the magnitude of the total orbital angular momentum for the largest permitted value of l?

    2. Relevant equations
    n>l, l is bigger or equal to m

    3. The attempt at a solution
    The allowed l= 3,2,1
    The allowed m for largest l= 3,2,1,0,-1,-2,-3
    Total orbital angular momentum is the sum of all Lz or L^2?
    Ans, total= 3+2+1+0 +(-1)+(-2)+(-3)=0?
    L^2= 3(3+1)hbar
    What is the total orbital angular momentum?
    Please guide ,thanks
     
  2. jcsd
  3. Jan 1, 2014 #2

    vela

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    Read your textbook and notes and answer the following questions:
    1. What does ##\vec{L}^2## physically represent?
    2. What about ##L_z##?
    3. How are ##l## and ##m## related to ##\vec{L}^2## and ##L_z##?
     
  4. Jan 1, 2014 #3
    ##\vec{L}^2## mean the angular momentum square
    ##L_z## angular momentum in z direction
    ##\vec{L}^2##=l(l+1)\hbar and ##L_z##=m\hbar.
    Total orbit angular momentum is j?
    J=l-(1/2) or l+(1/2)
     
  5. Jan 1, 2014 #4

    vela

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    That should be ##\vec{L}^2=l(l+1)\hbar^2##. Total orbital angular momentum means not just the z-component. ##m## and ##l## are quantum numbers, not angular momenta.

    The key word here is orbital. Which observable corresponds to orbital angular momentum?
     
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