Measuring Angular Momentum for Free Particles: L-square =l(l+1)?

[sanjibghosh]

In case of 3d free particle Schrödinger 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?

 

[malawi_glenn]

you measure the angular momentum with respect to some reference point.

 

[sanjibghosh]

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?

 

[malawi_glenn]

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.

 

[sanjibghosh]

So when I will measure the angular momentum, I can get all the L-square with different probability..Is it true?

 

[malawi_glenn]

yes.

 

[sanjibghosh]

So, how can I know whether this is Boson or Fermion?

 

[malawi_glenn]

what has that anything to do with angular momentum?

 

[sanjibghosh]

but Boson or Fermion depends on it's angular momentum.

 

[malawi_glenn]

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

What you and me have discussed now is a particles orbital angular momentum.

 

[sanjibghosh]

OK thanks and sorry for the stupidity

 

[sanjibghosh]

But for the same reason, why is not energy quantized?

 

[malawi_glenn]

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.

 

[sanjibghosh]

just studying...

 

[quantum brain]

what is scattering theory?

 

[malawi_glenn]

http://www.isv.uu.se/thep/courses/QM/scattering-overview.pdf http://en.wikipedia.org/wiki/Scattering_theory

 

[sanjibghosh]

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).

 

[sanjibghosh]

and I only know the partial wave method.

 

[malawi_glenn]

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.

 

[sanjibghosh]

ok thanks..
actually my mother tongue is Bengali that's why I have some problem in English.