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

In summary, the conversation discusses the 3d free particle Schrodinger equation solution and its relationship to the quantization of angular momentum. The difficulty of measuring the angular momentum of a free particle without a potential is also addressed, as well as the concept of scattering and its role in energy conservation. The conversation ends with a clarification about the difference between orbital and intrinsic angular momentum and a request for the use of the "edit" feature due to language barriers.
  • #1
sanjibghosh
50
0
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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  • #2
you measure the angular momentum with respect to some reference point.
 
  • #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?
 
  • #4
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.
 
  • #5
So when I will measure the angular momentum, I can get all the L-square with different probability..Is it true?
 
  • #6
yes.
 
  • #7
So, how can I know whether this is Boson or Fermion?
 
  • #8
what has that anything to do with angular momentum?
 
  • #9
but Boson or Fermion depends on it's angular momentum.
 
  • #10
no, they depend on their INTRINSIC angular momentum; The Spin.

What you and me have discussed now is a particles orbital angular momentum.
 
  • #11
OK thanks and sorry for the stupidity
 
  • #12
But for the same reason, why is not energy quantized?
 
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  • #13
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.
 
  • #14
just studying...
 
  • #15
what is scattering theory?
 
  • #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).
 
  • #18
and I only know the partial wave method.
 
  • #19
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.
 
  • #20
ok thanks..
actually my mother tongue is Bengali that's why I have some problem in English.
 

1. What is angular momentum and why is it important in physics?

Angular momentum is a property of a rotating object or system and is defined as the product of its moment of inertia and its angular velocity. It is important in physics because it is a conserved quantity, meaning that it remains constant unless acted upon by an external torque. This makes it a useful tool for understanding the motion of objects and systems in rotational motion.

2. How is angular momentum measured for free particles?

Angular momentum for free particles can be measured using the equation L-square = l(l+1), where L is the total angular momentum and l is the quantum number representing the angular momentum of the particle. This equation is derived from the Schrödinger equation, which describes the quantum behavior of particles.

3. What is the significance of the value of l in the equation L-square = l(l+1)?

The value of l in the equation L-square = l(l+1) represents the angular momentum of the particle in terms of its quantum state. This value can range from 0 to n-1, where n is the principal quantum number. It provides information about the orientation and direction of the particle's motion.

4. Can angular momentum be measured for particles that are not in rotational motion?

Yes, angular momentum can still be measured for particles that are not in rotational motion. This is because angular momentum is a property of the particle itself, not just its motion. It can also be measured for particles in translational or vibrational motion.

5. How is angular momentum related to other fundamental quantities in physics?

Angular momentum is related to other fundamental quantities in physics, such as mass, velocity, and force. It is also related to energy, as it is a conserved quantity and can be converted into other forms of energy. In addition, it is related to the principle of conservation of angular momentum, which states that the total angular momentum of a closed system remains constant in the absence of external torques.

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