论文标题
径向schrödinger方程的统一，连续，固定扰动理论
Unitary, continuum, stationary perturbation theory for the radial Schrödinger equation
论文作者
论文摘要
如果统一转换将自由发生器与相互作用的相对论理论的发电机联系起来，那么庞加莱集团发电机的换向器将保持不变。我们测试了在非同性案例中发电机单一转变的概念，要求自由和相互作用的哈密顿人通过单一转变而相关。其他作者将此概念应用于时间依赖性的扰动理论，以使时间演化运算符的单位性在扰动理论中的每个顺序中，结果表明对标准扰动理论有所改善。在我们的案例中，可以构建固定的扰动理论，以找到径向Schrödinger方程的近似解，用于从球形对称势中散射。在耦合常数中，在第一和二阶的相移获得了一般公式。我们在一个具有已知精确解决方案的简单系统上测试该方法，并在我们对S波相移的一阶和二阶贡献之间找到完全一致的一致性，以及相应的扩展到精确解决方案的二阶。
The commutators of the Poincaré group generators will be unchanged in form if a unitary transformation relates the free generators to the generators of an interacting relativistic theory. We test the concept of unitary transformations of generators in the nonrelativistic case, requiring that the free and interacting Hamiltonians be related by a unitary transformation. Other authors have applied this concept to time-dependent perturbation theory to give unitarity of the time evolution operator to each order in perturbation theory, with results that show improvement over the standard perturbation theory. In our case, a stationary perturbation theory can be constructed to find approximate solutions of the radial Schrödinger equation for scattering from a spherically symmetric potential. General formulae are obtained for the phase shifts at first and second order in the coupling constant. We test the method on a simple system with a known exact solution and find complete agreement between our first- and second-order contributions to the s-wave phase shifts and the corresponding expansion to second order of the exact solution.
