单位矩阵的平方根与Dirac and Klein-Gordon方程组(英)

Square Roots of Identity Matrix and Dirac and Klein-Gordon Equations

此文是常州工业技术学院学报已经刊登的文章[5]的继续,包含有以下三方面的新结果。1.找出了单位矩阵的所有平方根。2.构造了Dirac方程初值问题的解。3.偶然发现了一些与Dirac方程的解有关的矩阵是4×4单位矩阵的一种特殊形式的平方根。此外本文利用Klein-Gordon算子分解为Dirac算子的平方的分解式给出了以下的两个注解:(1)Dirac方程的相对论不变性只是Klein-Gordon方程的相对论不变性的推论。(2)Dirac方程的基本解特征矩阵或解向量组是Klein-Gordon方程的解张量。最后也是最重要的,我们得到了一个新的公式(9.15)去计算量子力学中的S矩阵。

The paper is a continuation of the paper [5] and contains three new results; 1. Having found all square roots of an identity matrix. 2. Having structured the solutions of initial value problems of Dirac equations. 3. Having found quite by chance that some solution matrices of Dirac are square roots of 4×4 identity matrix. And secondly by using the factorization of Klein-Gordon operator to Dirac operators, the paper gives two notes: (1) the relativity of Dirac equation is a deduction of the relativity of Klein-Gordon equation, (2) the fundamental eigen matrices or solution vectors of Dirac equations are solution tensors of Klein-Gordon equation. Finally and more importantly we get a new formula (9. 15) to solve the so-called .S Matrix in quantum mechanics.