# Angular momentum of a free Dirac particle

• DOTDO
In summary, Dirac discovered the operator S in the Dirac equation which, when combined with the orbital angular momentum L, gives the total angular momentum J. This operator also gives an eigenvalue of spin 1/2, describing fermions. The total angular momentum remains constant in motion, but the individual values of L and S can vary over time even without an external force. However, if there is an external force, both L and S may change to account for the exchange of angular momentum with the external system.
DOTDO
Hi

for Dirac equation, [ L , H ] =/ 0 ,

so Dirac found a operator S such that

1. [ S , H ] = - [L, H] ---> [ J, H ] = 0 where J = L + S , the total angular momentum.

2. S gives an eigenvalue of spin 1/2 ---> solutions of Dirac equation describe fermions.
The total angular momentum is constant in motion...

but still, L and S varies as time elapses although there is no external force... why?And if there exists an external force, do L and S both change?

DOTDO said:
but still, L and S varies as time elapses although there is no external force... why?
This is an internal exchange of angular momentum and deals with internal interactions. If you had an interaction with an external system you might change the total angular momentum.

## 1. What is angular momentum?

Angular momentum is a physical quantity that measures the amount of rotational motion of a particle or system. It is a vector quantity, meaning it has both magnitude and direction.

## 2. What is a free Dirac particle?

A free Dirac particle is a particle described by the Dirac equation, a relativistic quantum mechanical equation that describes the behavior of fermions, such as electrons, in a vacuum. It takes into account the effects of special relativity and spin.

## 3. How is angular momentum calculated for a free Dirac particle?

The angular momentum of a free Dirac particle is calculated using the angular momentum operator, which is derived from the Dirac equation. This operator takes into account the spin and orbital angular momentum of the particle.

## 4. What is the significance of the angular momentum of a free Dirac particle?

The angular momentum of a free Dirac particle is an important quantity in quantum mechanics as it is conserved, meaning it remains constant in a closed system. It also plays a crucial role in the behavior and interactions of particles in the subatomic world.

## 5. How does the angular momentum of a free Dirac particle differ from that of a classical particle?

The angular momentum of a free Dirac particle differs from that of a classical particle in that it takes into account the particle's intrinsic spin, which is a quantum mechanical property. This means that the angular momentum of a free Dirac particle can only take on discrete values, unlike in classical mechanics where it can have any value.

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