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Free Particle

  1. Feb 19, 2009 #1
    In case of 3d free particle Schrodinger equation solution, the angular momentum eigenvalue L-square =l(l+1) and a free particle has a wavefunction as the superposition of all 'l'(angular momentum) states.Now the difficulty is that when I will measure the L-square, is it true that I will endup with a result L-squrae=l(l+1) even for a free particle? Can anybody measure the anguler momentum directly?
     
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  3. Feb 19, 2009 #2

    malawi_glenn

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    you measure the angular momentum with respect to some reference point.
     
  4. Feb 20, 2009 #3
    ok......but without potential how can I expect the angular momentum quantization? Is it experimentally verified that the angular momentum of a free particle is quantized?
     
  5. Feb 20, 2009 #4

    malawi_glenn

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    you write the plane wave as series expansion of angular momenta.

    in order to measure the angular momentum of a particle you need something to make it interact with, a potential ..

    but yes scattering of particles against potentials include terms for all angular momentum components of the incoming particle.
     
  6. Feb 22, 2009 #5
    So when I will measure the angular momentum, I can get all the L-square with different probability..Is it true?
     
  7. Feb 22, 2009 #6

    malawi_glenn

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  8. Feb 22, 2009 #7
    So, how can I know whether this is Boson or Fermion?
     
  9. Feb 22, 2009 #8

    malawi_glenn

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    what has that anything to do with angular momentum?
     
  10. Feb 22, 2009 #9
    but Boson or Fermion depends on it's angular momentum.
     
  11. Feb 22, 2009 #10

    malawi_glenn

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    no, they depend on their INTRINSIC angular momentum; The Spin.

    What you and me have discussed now is a particles orbital angular momentum.
     
  12. Feb 22, 2009 #11
    OK thanks and sorry for the stupidity
     
  13. Feb 22, 2009 #12
    But for the same reason, why is not energy quantized?
     
    Last edited: Feb 22, 2009
  14. Feb 22, 2009 #13

    malawi_glenn

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    the energy of a free particle is the initial energy...

    have you learned about scattering theory yet? If not, you might want to study it.
     
  15. Feb 22, 2009 #14
    just studying....
     
  16. Feb 22, 2009 #15
    what is scattering theory?
     
  17. Feb 22, 2009 #16

    malawi_glenn

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    Last edited by a moderator: May 4, 2017
  18. Feb 22, 2009 #17
    It is not so clear to me but I only know that this is the quantum mechanical description of scattering of some incoming particles by some scatterer (potential).
     
  19. Feb 22, 2009 #18
    and I only know the partial wave method.
     
  20. Feb 22, 2009 #19

    malawi_glenn

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    energy is conserved in inelastic scattering, i don't know where your "why is not energy quantized?" comes from - what makes you ask such question??

    use "edit" feature.
     
  21. Feb 22, 2009 #20
    ok thanks..
    actually my mother tongue is Bengali that's why I have some problem in English.
     
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