论文标题
引导Kronig-Penney模型
Bootstrapping the Kronig-Penney Model
论文作者
论文摘要
最近，已对共形场理论的引导方法进行了调整，用于研究各种量子机械系统的能量光谱。在本文中，我们考虑了这些方法在从Schrödinger方程中获得具有周期性势的光谱时的应用，特别注意一维晶格中粒子的Kronig-Penney模型。通过适当选择涉及位置和动量的操作员基础，我们发现Bootstrap方法有效地计算了能量谱的频带间隙，但有效地限制了最小能量。我们展示了如何应用更复杂的限制因素涉及较高的动量力量可以解决此类问题。我们还提出了一种分析构建与系统动量相关的分散关系的方法。
Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the Schrödinger equation with periodic potentials, paying particular attention to the Kronig-Penney model of a particle in a one-dimensional lattice. With an appropriate choice of operator basis involving position and momenta, we find that the bootstrap approach efficiently computes the band gaps of the energy spectrum but has trouble effectively constraining the minimum energy. We show how applying more complex constraints involving higher powers of momenta can potentially remedy such a problem. We also propose an approach for analytically constructing the dispersion relation associated with the Bloch momentum of the system.
