※ 引述《ed78617 (雞爪)》之銘言： : [領域]古典力學 (題目相關領域) : [來源] Goldstein (課本習題、考古題、參考書...) : [題目] : Show that a rotation about any given axis can be obtained as the product of : two successive rotations, each through 180° : [瓶頸] (寫寫自己的想法，方便大家為你解答) : 請教一下要如何下手 : 是利用球面三角形的餘弦律和正弦律嗎？ : 先謝謝各位~ 太久沒碰古力了 我用量子力學證明 Take two 3-d unit vector n1 and n2. in the case of n1˙n2 = cos(γ) and n1×n2=n3*sin(γ), γ the angle between two vectors and n3 is the unit vector orth. to n1 and n2. A vector V after a rotation around n1 by π becomes exp(-iσ˙n1*π) V exp(iσ˙n1*π/2), where σ is the Pauli matrix By using exp{iσ˙n1*π}=cos(π/2)+i*sin(π/2)*(σ˙n1)=i*(σ˙n1) (-1)*exp{iσ˙n1*π}*exp{iσ˙n2*π} = (σ˙n1)(σ˙n2) =1 (n1˙n2) + i σ˙(n1×n2) = cos(γ) + i (σ˙n3) sin(γ) = exp{i(σ˙n3)*γ}, which stands for a rotation about the n3-axis by 2*γ. --

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