Quaternionic factorization of the Schrödinger operator and its applications to some first-order systems of mathematical physics
Quaternionic factorization of the Schrödinger operator and its applications to some first-order systems of mathematical physics
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DOI：
10.1088/0305-4470/36/44/008
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发表时间：
2003-05
期刊：
影响因子：
--
通讯作者：
V. Kravchenko;V. Kravchenko
中科院分区：
文献类型：
--
作者：
V. Kravchenko;V. Kravchenko
我们表明，一个丰富的一类物理上有意义的偏微分系统的一阶，如狄拉克方程与不同的一个组件的潜力，静态麦克斯韦的系统和系统描述的无力磁场相当于一个单一的四元数方程，这又减少了一般的薛定谔方程与四元数的潜力，并在某些情况下，这最后可以对角化。丰富多样的方法开发的不同问题对应的薛定谔方程可以应用到本工作中考虑的系统。
We show that an ample class of physically meaningful partial differential systems of first order such as the Dirac equation with different one-component potentials, static Maxwell's system and the system describing the force-free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a Schrodinger equation with quaternionic potential, and in some situations this last can be diagonalized. The rich variety of methods developed for different problems corresponding to the Schrodinger equation can be applied to the systems considered in the present work.