Spin: Fermions vs. Bosons - Explaining its Significance

[sruthisupriya]

what exactly is spin? why is it half integral for fermions and integral for bosons?what is the significance of the values?

 

[arivero]

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.

 

[marlon]

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

 

[marlon]

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


marlon