S^2 operator and its matrix representation in the spin-1/2 system

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The general definition of the S^2 operator, which we then calculate from the 3 directional operators for a spin-1/2 system.
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Thank you so much, this video is so clear and useful.

PerezInc
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Hi :), I have a question. This theory is equal to S= 1/2 or is completely diffetent. Thanks for tour response

yulitarami