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Angular momentum in whole numbers

  1. May 30, 2009 #1
    The dimension of Planck's constant h (ML2/T) is also the dimension of angular momentum. Does it follow that the angular momentum of any object must be hn where n is an integer? I know h was discovered in a different context, but I was just wondering.
     
  2. jcsd
  3. May 30, 2009 #2

    clem

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    It follows from quantum mechanics, not just the units, that L=nh.
    For a classical object, n is so large that L appears continuous.
     
  4. May 30, 2009 #3
    Here's the problem I'm having - consider the following scenario:

    Using a standard Cartesian coordinate system, a particle of mass m moves along the x axis in the positive x direction with constant speed v.

    Using (0,y) as a reference point (and assuming that v<<c) the scalar value of the particle's angular momentum is ymv. If angular momentum is always hn - where n is an integer - it follows that the particle's speed must be hn/ym.

    Since our reference point is arbitrary we can change it to 2y and this would make the allowable speeds of the particle be hn/2ym, which of course includes speeds not included in the set hn/ym.

    Since nothing has changed with the particle, why would it now have a different set of allowable speeds?
     
  5. May 31, 2009 #4

    alxm

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    Angular momentum would be in terms of h-bar, rather.
     
  6. May 31, 2009 #5

    clem

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    Yes, it should be hbar, but I was using units with 2pi=1.
    Snoopie, your problem is you are trying to use a classical impact parameter with a quantum trajectory. There is no fixed y.
     
  7. May 31, 2009 #6
    So angular momentum, action, or any other physical quantity with that dimension is precisely defined while all others (distance, energy, etc.) are not?
     
  8. May 31, 2009 #7

    atyy

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    Orbital angular momentum, spin angular momentum. Each are defined by the commutation relations. Spin can be half integer.
     
  9. May 31, 2009 #8
    I'm sorry; I guess I don't really understand even the most basic ideas of quantum mechanics - I thought I did.

    Is it the case that y should be replaced with y + Δy and (if the mass m is known with certainty) v should be replaced by v + Δv such that

    [tex]

    m \Delta y \Delta v = \hbar

    [/tex]

    while the angular momentum L = m (y + Δy) (v + Δv) is still known to be exactly [itex] n \hbar [/itex] ?
     
  10. May 31, 2009 #9

    clem

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    No, its more detailed than that. The particle moving is like an ocean wave. How would you describe the position of a wave? You need to look at a simple QM text.
     
  11. May 31, 2009 #10
    Is there a specific one you have in mind?
     
  12. May 31, 2009 #11

    atyy

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    Last edited by a moderator: Apr 24, 2017
  13. May 31, 2009 #12
    Thanks atyy. You always provide great resources!
     
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