同时求解Dirac和Ricatti方程
Solving simultaneously Dirac and Ricatti equations
摘要：
本文分析了具有Lorentz标量势的$d=1+1$中Dirac方程的行为。由于该系统是已知的超对称量子力学的物理实现，我们利用因式分解方法，以扩大限制类的可解问题。准确地说，它足以集成Ricatti方程，以构建单参数族的可解势。为了说明一个简单但相关的上下文中的程序，我们求助于一个模型，已被证明是有用的费米子数分馏的现象。
英文摘要：
We analyse the behaviour of the Dirac equation in $d=1+1$ with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise, it suffices to integrate a Ricatti equation to construct one-parameter families of solvable potentials. To illustrate the procedure in a simple but relevant context, we resort to a model which has proved useful in showing the phenomenon of fermion number fractionalization.
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