Schroedinger算子的四元数因子分解及其对某些一阶数学物理系统的应用
Quaternionic factorization of the Schroedinger operator and its applications to some first order systems of mathematical physics
摘要：
我们考虑下列一阶数学物理系统。1.具有标量势的狄拉克方程。2.具有电势的狄拉克方程。3.具有赝标势的狄拉克方程。4.描述具有非常数比例因子的非线性无力磁场或贝尔特拉米场的系统。5.缓变介质的麦克斯韦方程组。6.静态麦克斯韦系统。我们表明，所有这些品种的一阶系统减少到一个单一的四元数方程的分析，这反过来又减少到解决方案的薛定谔方程与biquaternionic潜在的。在某些重要的情况下，双四元数势可以对角化并转化为标量势。
英文摘要：
We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing non-linear force free magnetic fields or Beltrami fields with nonconstant proportionality factor. 5.The Maxwell equations for slowly changing media. 6.The static Maxwell system. We show that all this variety of first order systems reduces to a single quaternionic equation the analysis of which in its turn reduces to the solution of a Schroedinger equation with biquaternionic potential. In some important situations the biquaternionic potential can be diagonalized and converted into scalar potentials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
