标题： 量子力学在有限点数的空间中 显示英文标题

标题： Quantum Mechanics in a Space with Finite Number of Points

摘要： 我们为具有有限点数的离散位置空间定义了一个变形的动能算符。 结构可以是周期性的或非周期性的，并且有明确的端点。 结果表明，在非周期性情况下，由于端点的存在，平移算符变得非么正。 这唯一地定义了一个具有所需唯一表示的代数。 找到了两种情况下的能量本征值和能量波函数。 正如预期的那样，在连续极限下，非周期性情况的解与无限一维方势阱的解相同，而周期性情况的解则与具有周期性边界条件的粒子在箱中的解相同。 显示英文摘要

摘要： We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the translation operator becomes nonunitary due to the end points. This uniquely defines an algebra which has the desired unique representation. Energy eigenvalues and energy wave functions for both cases are found. As expected, in the continuum limit the solution for the nonperiodic case becomes the same as the solution of an infinite one dimensional square well and the periodic case solution becomes the same as the solution of a particle in a box with periodic boundary conditions.