Re: [請益] 關於Pauli matrices
※ 引述《njvulfu (njvulfu)》之銘言：
: 各位大大好，
: 小弟初學量力，
: 對於Pauli matrices σ有一些不解之處，
: 所以，想請問：
: det(σ)=-1 & Tr(σ)=0 ，
: 以上這兩個特性有無任何物理意義？
我應該寫清楚一些
e^{iσ‧a} belongs to SU(2)
we call σ the generators of SU(2)
Why U ? because probability is conserved.
Why S ? because it comes from proper rotation.
then e^{-iσ^h‧a} e^{iσ‧a} = I
hence σ hermitian (sorry, ren1072 is right)
det(e^{iσ‧a}) = 1 = lim_{N→∞} det(I+(iσ‧a)/N)^N
=lim(1 + Tr(iσ‧a)/N + O(1/N^2))^N = e^{Tr(iσ‧a)}
hence, Tr(iσ‧a) = 0
however, a is arbitrary, then σ traceless
可查關鍵字 SU(2)
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※ 編輯: JohnMash 來自: 27.147.57.77 (12/10 20:22)
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