束缚态和能带结构--量子Hamilton - Jacobi方法的统一处理
Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach
摘要：
我们通过量子Hamilton-Jacobi方法分析了Scarf势，它同时表现出离散的能量束缚态和能带。一旦问题被映射到另一个准精确可解量子问题的零能量扇区，上述方法中的奇异性结构和边界条件自然地隔离了束缚态和周期态。能量本征值的获得，而无需求解相应的本征函数显式。我们还演示了如何找到本征函数，通过这种方法。
英文摘要：
We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate the bound and periodic states, once the problem is mapped to the zero energy sector of another quasi-exactly solvable quantum problem. The energy eigenvalues are obtained without having to solve for the corresponding eigenfunctions explicitly. We also demonstrate how to find the eigenfunctions through this method.
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。
