Natural Science Forum / Physics / Particle Physics / August 2005

We can calculate spin using the following equation:

where,

sv is the quantized spin vector,

s is the spin quantum number, which can be any non negative integer,

Given an arbitrary direction z (usually determined by an external
magnetic field) the spin z-projection is given by

Sz = ms.hbar

ms is the secondary spin quantum number, ranging from -s to +s in steps
of 1. This generates 2s+1 different values of ms.

The above is from wiki, see
http://en.wikipedia.org/wiki/Spin_quantum_number

Why should only non-negative values be allowed?

If we allow negative values, we get the following results.

s = 2, s+1 = 3, sv = 2.583162537E-34
s = 1.5, s+1 = 2.5, sv = 2.042169296E-34
s = 1, s+1 = 2, sv = 1.491389586E-34
s = 0.5, s+1 = 1.5, sv = 9.132858735E-35
s = 0, s+1 = 1, sv = 0
s = -0.5, s+1 = 0.5, sv = -5.272858449E-35
s = -1, s+1 = 0, sv = 0
s = -1.5, s+1 = -0.5, sv = 9.132858735E-35
s = -2, s+1 = -1, sv = 1.491389586E-34
s = -2.5, s+1 = -1.5, sv = 2.042169296E-34
s = -3, s+1 = -2, sv = 2.583162537E-34

As you can see, the origin is not s=0 but s=-0.5.
You can also see that the table is symmetric in regards to sv.
The table also shows the following:

For a spin -1/2 particle, s=-0.5, diff = 0
For a spin 0 particle, s=0 and s=-1, diff = 1
For an electron, s=0.5 and s=-1.5, diff = 2
For a photon, s=1 and s=-2, diff = 3
For a spin 3/2 particle, s=1.5 and s=-2.5, diff = 4
For a spin 2 particle, s=2 and s=-3, diff = 5

You should also notice that for the origin(s=-0.5):

sv = -(hbar/2)
Sz = +/-(hbar/2)

Since spin is given in terms of hbar/2, I think this highly
significant.

Any feedback welcome.