
#1
Jul2806, 11:53 AM

P: 424

Why is the spin quantum number given a value 1/2? Why not any other value, say +1 for clockwise spin and 1 for anticlockwise spin instead of +1/2 for clockwise spin and 1/2 for anticlockwise spin ?




#2
Jul2806, 04:32 PM

P: 546

This prescription takes [tex]\hbar[/tex] as the fundamental unit of angular momentum. So, what's really happening is that spin up has angular momentum [tex]\frac{\hbar}{2}[/tex] and spin down has [tex]\frac{\hbar}{2}[/tex].
In general this is a matter of convenience, as it is simply defined to be consistent with the use of [tex]\hbar[/tex] as the fundamental unit of angular momentum elsewhere. 



#3
Jul2806, 11:45 PM

Emeritus
Sci Advisor
PF Gold
P: 11,154

This is not just a convention chosen for convenience. The [itex]\pm \hbar/2 [/itex] comes from the eigenvalues equations for a spin1/2 particle (like the electron). A spin1 particle has eigenvalues, 1, 0 and 1, and so on...




#4
Jul2906, 01:18 PM

P: 424

Spin quantum number 



#5
Jul3006, 09:39 AM

P: 777

It is imposible to know two coordinates of the spin at the same time because of the restriction of the Uncertainty principle. So the number of eigenvalues give the number of observable states of a particle which is also subject to cetain selection rules. 



#6
Jul3006, 10:15 AM

Emeritus
Sci Advisor
PF Gold
P: 11,154





#7
Jul3006, 01:40 PM

P: 4,008

An electron has a spin (intrinsic angular momentum), but it does NOT actually rotate around its axis, guys. The 'rotational nature' of spin comes from the behavior of the Dirac wavefunction (this is a matrix that represents a physical state and arises when solving the Dirac equation. This equation describes a fermion : a particle with noninteger spin) under coordinatetransformations (which are called the rotations). With behavior i mean : how does the physics change if we interchange the components of this Dirac spinor, if we change the parity, if we apply coordinate transformations to the wavefunction and so on....For example, if we rotate the wavefunction 360°, do we still get the same physical laws...You see the pattern ??? It is this specific behavior that yields the name SPINOR because if you rotate it 360°, you get the opposite value. Now, changing coordinates (represented by rotations) and looking how the physics changes or not, is NOT THE SAME as actually rotating. So, spin arises thanks to symmetries involved but there is no actual rotation. marlon 


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