Spin, orbital, and total angular momentum
Main article: Spin (physics)
Angular momenta of a classical object.
Left: "spin" angular momentum S is really orbital angular momentum of the object at every point,
right: extrinsic orbital angular momentum L about an axis,
top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω),[28]
bottom: momentum p and its radial position r from the axis.The total angular momentum (spin plus orbital) is J. For a quantum particle the interpretations are different; particle spin does not have the above interpretation.
The classical definition of angular momentum as L = r × p {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} } \mathbf {L} =\mathbf {r} \times \mathbf {p} can be carried over to quantum mechanics, by reinterpreting r as the quantum position operator and p as the quantum momentum operator. L is then an operator, specifically called the orbital angular momentum operator.
However, in quantum physics, there is another type of angular momentum, called spin angular momentum, represented by the spin operator S. Almost all elementary particles have spin. Spin is often depicted as a particle literally spinning around an axis, but this is a misleading and inaccurate picture: spin is an intrinsic property of a particle, unrelated to any sort of motion in space and fundamentally different from orbital angular momentum. All elementary particles have a characteristic spin, for example electrons have "spin 1/2" (this actually means "spin ħ/2") while photons have "spin 1" (this actually means "spin ħ").
Finally, there is total angular momentum J, which combines both the spin and orbital angular momentum of all particles and fields. (For one particle, J = L + S.) Conservation of angular momentum applies to J, but not to L or S; for example, the spin–orbit interaction allows angular momentum to transfer back and forth between L and S, with the total remaining constant. Electrons and photons need not have integer-based values for total angular momentum, but can also have fractional values.[29]
https://en.wikipedia.org/.../File:Classical_angular...
Main article: Spin (physics)
Angular momenta of a classical object.
Left: "spin" angular momentum S is really orbital angular momentum of the object at every point,
right: extrinsic orbital angular momentum L about an axis,
top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω),[28]
bottom: momentum p and its radial position r from the axis.The total angular momentum (spin plus orbital) is J. For a quantum particle the interpretations are different; particle spin does not have the above interpretation.
The classical definition of angular momentum as L = r × p {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} } \mathbf {L} =\mathbf {r} \times \mathbf {p} can be carried over to quantum mechanics, by reinterpreting r as the quantum position operator and p as the quantum momentum operator. L is then an operator, specifically called the orbital angular momentum operator.
However, in quantum physics, there is another type of angular momentum, called spin angular momentum, represented by the spin operator S. Almost all elementary particles have spin. Spin is often depicted as a particle literally spinning around an axis, but this is a misleading and inaccurate picture: spin is an intrinsic property of a particle, unrelated to any sort of motion in space and fundamentally different from orbital angular momentum. All elementary particles have a characteristic spin, for example electrons have "spin 1/2" (this actually means "spin ħ/2") while photons have "spin 1" (this actually means "spin ħ").
Finally, there is total angular momentum J, which combines both the spin and orbital angular momentum of all particles and fields. (For one particle, J = L + S.) Conservation of angular momentum applies to J, but not to L or S; for example, the spin–orbit interaction allows angular momentum to transfer back and forth between L and S, with the total remaining constant. Electrons and photons need not have integer-based values for total angular momentum, but can also have fractional values.[29]
https://en.wikipedia.org/.../File:Classical_angular...
Hla Myint Angular
momenta of a classical object. Left: "spin" angular momentum S is
really orbital angular momentum of the object at every point, right:
extrinsic orbital angular momentum L about an axis, top: the moment of
inertia tensor I and angular velocity ω (L is not always parallel to
ω),[28] bottom: momentum p and its radial position r from the axis.The
total angular momentum (spin plus orbital) is J. For a quantum particle
the interpretations are different; particle spin does not have the above
interpretation.
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