またt1{\displaystylet_{1}}を任意の時刻として、U(t,t1)U(t1,t0)=U(t,t0){\displaystyleU(t,t_{1})U(t_{1},t_{0})=U(t,t_{0})\}という関係が常に成り立つ。
所以，时间演化算符必须满足闭包性：U(t,t0)=U(t,t1)U(t1,t0){\displaystyleU(t,\,t_{0})=U(t,\,t_{1})U(t_{1},\,t_{0})}。