Orbital Angular Momentum Origin

In summary, angular momentum depends on origin, but in quantum mechanics one can calculate it for an electron orbiting an atom without specifying the axis.
  • #1
widderjoos
21
0
We know from classical mechanics that angular momentum [itex]L = r \times p[/itex] depends on your choice of origin. My question is: How does this work quantum mechanically? We know we get certain eigenvalues, but does this apply only in a certain choice of origin? How do we calculate angular momentum at some other point? I had a similar problem concerning torque on a magnetic dipole, [itex]\tau = \mu \times B = r \times F[/itex]. About what point do we measure the moment arm?
Do we just assume our origin is at the "center" of the orbit?

Thanks for the help.
 
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  • #2
widderjoos said:
We know from classical mechanics that angular momentum [itex]L = r \times p[/itex] depends on your choice of origin. My question is: How does this work quantum mechanically? We know we get certain eigenvalues, but does this apply only in a certain choice of origin? How do we calculate angular momentum at some other point? I had a similar problem concerning torque on a magnetic dipole, [itex]\tau = \mu \times B = r \times F[/itex]. About what point do we measure the moment arm?
Do we just assume our origin is at the "center" of the orbit?

Thanks for the help.

Angular momentum depends on position like in classical mechanics. However, when speaking of L e.g. for an atom, one always refers to the angular momentum of the atom in the rest frame of its center of mass so that L becomes independent of position. In principle it would be more appropriate to talk of a contribution to the spin of the compound particle than of angular momentum.
 
  • #3
In quantum mechanics, orbital angular momentum usually describes electron orbitals, where orbitals are located in an atom. When we regarding to an atom, I don't think choosing an arbitrary axis, say the tree trunk outside, would mean any thing to solving problems.

Therefore, it has no necessity to specify the axis, since we all know what we are referring to
 
  • #4
Yeah, that's what I was thinking, but just wanted to make sure since I couldn't find it explicitly stated anywhere. Thanks!
 

1. What is orbital angular momentum and where does it come from?

Orbital angular momentum is a fundamental physical property of a system that describes the rotational motion of particles around a central point or axis. It is a result of the combination of the individual angular momenta of the particles in the system.

2. How is orbital angular momentum different from spin angular momentum?

While both orbital and spin angular momentum involve rotational motion, they are fundamentally different. Orbital angular momentum is associated with the motion of particles around a central point, while spin angular momentum is an intrinsic property of a particle that describes its spin or rotation on its own axis.

3. What is the origin of the term "orbital" in orbital angular momentum?

The term "orbital" refers to the orbit of a particle or system of particles around a central point. In the context of orbital angular momentum, it describes the motion of particles around a central point due to the influence of a central force, such as gravity or electrostatic force.

4. How is orbital angular momentum conserved in a system?

According to the law of conservation of angular momentum, the total angular momentum of a closed system remains constant. In the case of orbital angular momentum, this means that the sum of the individual angular momenta of particles in the system, as well as their interactions, remains constant over time.

5. What are some applications of orbital angular momentum?

Orbital angular momentum has many important applications in physics, including in the study of atomic and molecular structures, as well as in the field of optics and quantum mechanics. It is also utilized in technologies such as satellite communications and navigation systems.

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