密度矩阵：p(t)=l山(t)》地(t)川 p(t)=lw(t)》((t川=p(t) Po()=(olw()》Iw()lo）=co(t)c(t) Poo(t)=Ica(t)12 对角元：处于σ〉态的几率 Trp}=∑poa0=∑lcaP=l p2(t)=l地(t)》((t)w(t)》(w(t)川=lw(t)》×1×(w(t川=p(t) ia,p=[i访alw(t)月w()训+lw(t)[iha,(w(t)川=[-i访a,w()]f =Hw()》w(t)川-lw(t)》w()A=A()-(t)A ihap(t)[H,p(t)] 霉可以用密度矩阵今来代替波函数 密度矩阵：𝜌ˆ(𝑡) = |𝜓(𝑡)ih𝜓(𝑡)| 𝜌 † (𝑡) = |𝜓(𝑡)ih𝜓(𝑡)| = 𝜌(𝑡) 𝜌𝜎 𝜎0 (𝑡) = h𝜎|𝜓(𝑡)ih|𝜓(𝑡)|𝜎 0 i = 𝑐𝜎 (𝑡)𝑐 ∗ 𝜎0 (𝑡) 𝜌𝜎 𝜎 (𝑡) = |𝑐𝜎 (𝑡)|2 ✞ ✝ ☎ ✆ 对角元：处于 |𝜎i 态的几率 𝑇𝑟{𝜌(𝑡)} = ∑ 𝜎 𝜌𝜎 𝜎 (𝑡) = ∑ 𝜎 |𝑐𝜎 (𝑡)|2 = 1 𝜌 2 (𝑡) = |𝜓(𝑡)ih𝜓(𝑡)|𝜓(𝑡)ih𝜓(𝑡)| = |𝜓(𝑡)i × 1 × h𝜓(𝑡)| = 𝜌(𝑡) 𝑖ℏ𝜕𝑡 𝜌ˆ = [𝑖ℏ𝜕𝑡 |𝜓(𝑡)i] h𝜓(𝑡)| + |𝜓(𝑡)i [𝑖ℏ𝜕𝑡h𝜓(𝑡)|] ✞ ✝ ☎ ✆ = [−𝑖ℏ𝜕𝑡 |𝜓(𝑡)i]† = H | ˆ 𝜓(𝑡)ih𝜓(𝑡)| − |𝜓(𝑡)ih𝜓(𝑡)|Hˆ = Hˆ 𝜌ˆ(𝑡) − 𝜌ˆ(𝑡)Hˆ 𝑖ℏ𝜕𝑡 𝜌ˆ(𝑡) = [Hˆ , 𝜌ˆ(𝑡)] ☞可以用密度矩阵 𝜌ˆ 来代替波函数