Spin: Fermions vs. Bosons - Explaining its Significance

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In summary: Ps: In summary, spin is a mathematical phenomena that arises from the fact that QM is invariant under rotations. It is used to label objects that behave in a "certain way" under rotations.
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sruthisupriya
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what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?
 
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sruthisupriya said:
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?

One could say it is a mathematical phenomena infiltering into a physicist party. When you look to shroedinger equation for rotationally symmetric situations you get a quantun number, j, which must be a integer multiple of Planck constant. But when you look at born-heisenberg-jordan matrix quantum mechanics, you find that rotational symmetry allows for half-integer multiples too.
 
  • #3
sruthisupriya said:
what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?
Hi

On a more mathematical level, spin arises due to the fact that QM (and physics in general) is invariant under rotations. For example, suppose you know the expectation value of some QM observable that depends on the x, y and z coordinates. If you perform a rotation onto these coordinates, the expectation value cannot change. It must have the same value before and after the rotation has been performed. Hence, you have invariance under rotations.

If this property is respected (and it is ofcourse) the wavefunctions must behave in a "certain way" under rotations. "Certain way" means that if you rotate them over 360 degrees, you get the opposite value. Do this again and you get the same initial value. Objects that behave this way under rotations are called spinors and the spin quantumnumber is a number that labels such spinors.

Keep in mind that spin has nothing to do with atoms rotating along some axis. The link with rotations is that of "invariance under rotations" so it is not the object that is rotating but the coordinates !

regards
marlon
 
  • #4
Ps : Check the "elementary particles presented" thread. We define spin in a more indept (ie full grouptheoretical definition) way there.


marlon
 

Related to Spin: Fermions vs. Bosons - Explaining its Significance

1. What is the difference between fermions and bosons?

Fermions and bosons are two types of subatomic particles. Fermions have half-integer spin, while bosons have integer spin. This means that fermions have an intrinsic angular momentum that is a multiple of 1/2 (such as 1/2, 3/2, 5/2), while bosons have an intrinsic angular momentum that is a multiple of 1 (such as 1, 2, 3). This fundamental difference in spin leads to different properties and behaviors of these particles.

2. What is the significance of spin in physics?

Spin is a fundamental property of particles and plays a crucial role in determining their behavior and interactions. It is a quantum mechanical property that describes the intrinsic angular momentum of a particle. Spin also dictates the allowed energy states of a particle and is responsible for the stability of matter.

3. Why are fermions and bosons classified as different types of particles?

Fermions and bosons have distinct characteristics and behaviors due to their different spin values. Fermions follow the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state at the same time. On the other hand, bosons can occupy the same quantum state, leading to phenomena such as Bose-Einstein condensation and superfluidity.

4. How are fermions and bosons relevant in the study of matter and energy?

Fermions make up matter particles, such as protons, neutrons, and electrons. These particles have half-integer spin and follow the rules of quantum mechanics, making them essential for understanding the behavior of atoms and molecules. On the other hand, bosons are carriers of fundamental forces, such as photons for the electromagnetic force and gluons for the strong nuclear force. These particles have integer spin and their interactions play a crucial role in understanding the fundamental forces of nature.

5. Can fermions and bosons interact with each other?

Yes, fermions and bosons can interact with each other, but their interactions are constrained by their spin values. Fermions can only interact with other fermions through the exchange of bosons, while bosons can interact with both fermions and other bosons. This interaction between particles with different spin values is crucial in understanding the behavior and properties of matter and energy.

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