Query about spin and uncertainty

I am looking at a portion of a Wiki article at the link below:

http://en.wikipedia.org/wiki/Spin_quantum_number#Algebra

It says:

"The algebraic theory of spin is a carbon copy of the Angular momentum
in quantum mechanics theory. First of all, spin satisfies the
fundamental commutation relation:
[S_i,S_j] = i hbar eta_ijk S_k, [S_i,S^2]=0

This means that is impossible to know two coordinates of the spin at the
same time *because of the restriction of the Uncertainty principle.*"
(emphasis added)

I would appreciate if someone can elucidate the most direct connection
between

[S_i,S_j] = i hbar eta_ijk S_k (1)

and the uncertainty principle in the form:

[x,p] = i hbar (2)

or any other suitable form. Is there a direct, one-step jump that can
be made from (1) right to (2)? Or, can someone write down a calculation
which shows the most direct and transparent path from (1) to (2)? Keep
it as simple and direct as possible.

Thanks,

Jay.
____________________________
Jay R. Yablon
Email: jyablon@xxxxxxxxxxxx
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm


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Relevant Pages

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  • Re: Query about spin and uncertainty
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