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创建时空可变系多线矢物理学(106)通常量子力学和场论的相应改造和发展(4) 任意函数[F(A(X,n)(x))],[F(B(X,n)(x))]的平均值
(接(105))
4维时空 n维多线矢对子[矢A(X,n)],[矢B(X,n)]各分量模长,A(X,n)(x), B(X,n)(x),的任意函数[F(A(X,n))],[F(B(X,n))]的平均值分别为:
[F(A(X,n))平均值]={[F(A(X,n))(F’(A(X,n),B(X,n)))^2 dR(X,n)}R(X,n)积分
/{(F’(A(X,n),B(X,n)))^2 dR(X,n)}R(X,n)积分
={F’*(A(X,n),B(X,n))[F(A(X,n))F’(A(X,n),B(X,n)) dR(X,n)}R(X,n)积分
/{(F’(A(X,n),B(X,n)))^2 dR(X,n)}R(X,n)积分,
[F(B(X,n))平均值]={[F(B(X,n))(F’(A(X,n),B(X,n)))^2 dR(X,n)}R积分
/{(F’(A(X,n),B(X,n)))^2 dR(X,n)}R积分
={F’*(A(X,n),B(X,n))[F(B(X,n))F’(A(X,n),B(X,n)) dR(X,n)}R积分
/{(F’(A(X,n),B(X,n)))^2 dR(X,n)}R积分,
分别在4维时空的全部位置或动量空间 ,R(X,n)或p(X,n),找到由n维多线矢对子A(X,n); B(X,n)表达的粒子的几率=1,即有:
{(F’(A(X,n),B(X,n)))^2 dR(X,n)}R(X,n)全积分
={(F’(A(X,n),B(X,n)))^2 dP(X,n)}P(X,n)全积分,
[F(A(X,n))平均值]全={[F(A(X,n))(F’(A(X,n),B(X,n)))^2 dR(X,n)}R(X,n)全积分
={F’*(A(X,n),B(X,n))[F(A(X,n))F’(A(X,n),B(X,n)) dR(X,n)}R(X,n)全积分
[F(B(X,n))平均值]全={[F(B(X,n))(F’(A(X,n),B(X,n)))^2 dR(X,n)}R全积分
={F’*(A(X,n),B(X,n))[F(B(X,n))F’(A(X,n),B(X,n)) dR(X,n)}R全积分
[F(A(X,n))平均值]全={[F(A(X,n))(F’(A(X,n),B(X,n)))^2 dP(X,n)}P(X,n)全积分
={F’*(A(X,n),B(X,n))[F(A(X,n))F’(A(X,n),B(X,n)) dP(X,n)}P(X,n)全积分
[F(B(X,n))平均值]全={[F(B(X,n))(F’(A(X,n),B(X,n)))^2 dP(X,n)}P全积分
={F’*(A(X,n),B(X,n))[F(B(X,n))F’(A(X,n),B(X,n)) dP(X,n)}P全积分
也可将其各分量模长分别用相应的算符取代,而得相应的算符各式。
因而,4维时空 n维多线矢对子[矢A(X,n)], [矢B(X,n)],各分量模长, A(X,n)(x), B(X,n)(x),的任意函数, F(A(X,n)(x)), F(B(X,n)(x)), 的平均值也可按“算符”运算。
(未完待续)
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