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创建时空可变系多线矢物理学(111)通常量子力学和场论的相应改造和发展(8)
波函数F’随时间的变化, (n维) 多线矢 的Schrodinger方程,
(接(110))
F’([矢A(X,n)],[矢B(X,n)])=F’0exp(i[矢A(X,n)]点乘[矢B(X,n)]/h),
其对时间的导数:
dF’/dt(X(n))=(1/h)[矢D(X(n))]F’点乘[时间导数A(X,n)(x)]
={([偏A(X,n)(x)]F’)[时间导数A(X,n)(x)][基矢(X,n)(x)], (x)=(x)1到(x)n求和},
对大量粒子进行统计的量子力学和场论,(n维)多线矢可用相应的算符取代,即:
[符矢A(X,n)(x)]=[矢A(X,n)(x)]=A(X,n)(x)[基矢(X,n)(x)],
[符矢A(X,n)]={[符矢A(X,n)(x)], (x)=(x)1到(x)n求和},
[矢D(X(n))]={W(A(X,n)(x))[偏A(X,n)(x)][基矢(X,n)(x)], (x)=(x)1到(x)n求和},
[符矢B(X,n)(x)]=[矢B(X,n)(x)]=A(X,n)(x)[基矢(X,n)(x)],
[符矢B(X,n)]={[符矢B(X,n)(x)], (x)=(x)1到(x)n求和},
[符矢B(X,n)(x)]=ih[偏A(X,n)(x)][基矢(X,n)(x)],
[矢B(X,n)(x)]=m(X,n)[时间导数矢A(X,n)(x)]
=m(X,n)W(A(X,n)(x)) [时间导数A(X,n)(x)] [基矢(X,n)(x)],
上式成为:
dF’/ dt(X(n))= [时间导数矢A(X,n)(x)]点乘([矢D(X(n))]F’)
={[时间导数A(X,n)(x)][偏A(X,n)(x)]F’, (x)=(x)1到(x)n求和}
=(i/(hm(X,n))[符矢B(X,n)]点乘[符矢B(X,n)]F’
=-(i/(hm(X,n)){ [偏A(X,n)(x)]F’, (x)=(x)1到(x)n求和}
这就是推广到大量自由粒子相互匹配成对的各类(n维)多线矢[矢A(X,n)],[矢B(X,n)]的Schrodinger方程, 它也是相应的量子力学的重要基础之一。
(未完待续)
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