Is the Formula for Spin Also True for Angular Momentum?

In summary, the known formula for the spin is S=0.5*h*\sigma. While this formula may also apply to the orbital angular momentum (L) and total angular momentum, there are additional restrictions for the orbital angular momentum due to the Heisenberg commutation relations. These restrictions mean that only integer values are allowed for the eigenvalues of the orbital angular momentum. More information can be found in Ballentine's book, specifically on pages 169-170.
  • #1
Cosmossos
100
0
Hello
Here is the known formula for the spin: S=0.5*[STRIKE]h[/STRIKE]*[tex]\sigma[/tex]
is this formula correct also to the orbital Angular momentum (L) and to the total Angular momentum?
I think it is correct because S,L,J operators that belong to Lie algebra/group.
Is it true?
 
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  • #2
Cosmossos said:
Here is the known formula for the spin: S=0.5*[STRIKE]h[/STRIKE]*[tex]\sigma[/tex]
is this formula correct also to the orbital Angular momentum (L) and to the total Angular momentum?
I think it is correct because S,L,J operators that belong to Lie algebra/group.
Is it true?

No. The orbital angular momentum has a special form:

[tex]
{\bm L} ~=~ {\bm Q} ~\times~ {\bm P}
[/tex]

where Q and P satisfy the usual Heisenberg commutation relations.
This extra restriction causes a corresponding restriction in the
possible eigenvalues of orbital angular momentum, namely that
only integer values are allowed.

Details can be found in Ballentine, pp169-170.
 

FAQ: Is the Formula for Spin Also True for Angular Momentum?

What is the formula for spin and angular momentum?

The formula for spin is given by S = ħ/2√j(j+1), where ħ is the reduced Planck constant and j is the spin quantum number. The formula for angular momentum is given by L = Iω, where I is the moment of inertia and ω is the angular velocity.

How are spin and angular momentum related?

Spin and angular momentum are related because both quantities involve rotational motion. Spin is a fundamental property of particles, while angular momentum is a measure of the momentum of a rotating object.

Is the formula for spin the same as the formula for angular momentum?

No, the formula for spin and the formula for angular momentum are different. The formula for spin is specific to particles, while the formula for angular momentum applies to any rotating object.

Can the formula for spin be applied to all particles?

Yes, the formula for spin can be applied to all particles, including subatomic particles like electrons, protons, and neutrons. However, the value of the spin quantum number may vary depending on the particle.

What is the significance of the formula for spin and angular momentum?

The formula for spin and angular momentum play a crucial role in understanding the behavior of particles and objects in motion. They help explain and predict the rotational properties of particles and objects, and have many applications in various fields of science, such as quantum mechanics and astrophysics.

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