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From: JEMebius on 10 Dec 2009 05:15
hal2k wrote:
> Hello everyone;
>
> I have a little problem about spin matrix. How can make a 3d spin
> matrix from spin operators ? I have looked every where but I couldn't
> find a single example :(

Hint:
Spin matrices belong to the subject of "Matrix representations of the 3D rotation group
SO(3) and the special unitary group SU(2)".

Wolfgang Pauli was the most important physicist who developed and applied group
representation theory to particle physics. Please read and study his original lecture notes!

SU(2) is a two-fold cover of SO(3). That means, there exists a 2:1 analytic group
homomorphism of SU(2) onto SO(3). "Analytic" means that the mapping functions involved are
analytic functions, i.e. functions admitting a power series expansion at every point in
their domains.

Any advanced textbook on quantum mechanics treats spin and angular momentum. SO(3)
suffices to treat classical angular momentum; SU(2) is needed to describe spin properties.

See also for instance Wikipedia for "quantum mechanics", "representation theory",
"rotation group", "electron spin", "Pauli matrices", "angular momentum", "entanglement"
and related subjects.
And for the more mathematically oriented readers: "Lie group", "Lie algebra",
"Quaternions" etc.

Happy studies: Johan E. Mebius
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