论文标题
通过有限系列的正方形集成函数对结合状态进行逐渐近似
Progressive approximation of bound states by finite series of square-integrable functions
论文作者
论文摘要
我们使用“三角形表示方法”来以有限大小的基础集为结合状态的时间无关的schrödinger方程。我们获得了两类的解决方案作为有限的平方集成函数的有限系列，这些函数支持波动官的三角矩阵表示。差分方程成为该系列膨胀系数的代数三项递归关系，该关系是用能量和/或潜在参数中有限多项式求解的。这些正交多项式包含有关系统的所有物理信息。配置空间中的基础元素是根据Romanovski-Bessel多项式或Romanovski-Jacobi多项式编写的。两种多项式的最大程度受多项式参数的限制。这使得基本设置有限的大小足以使结合状态波置次数的近似值随着基尺寸的增加而改善。
We use the "tridiagonal representation approach" to solve the time-independent Schrödinger equation for bound states in a basis set of finite size. We obtain two classes of solutions written as finite series of square integrable functions that support a tridiagonal matrix representation of the wave operator. The differential wave equation becomes an algebraic three-term recursion relation for the expansion coefficients of the series, which is solved in terms of finite polynomials in the energy and/or potential parameters. These orthogonal polynomials contain all physical information about the system. The basis elements in configuration space are written in terms of either the Romanovski-Bessel polynomial or the Romanovski-Jacobi polynomial. The maximum degree of both polynomials is limited by the polynomial parameter(s). This makes the size of the basis set finite but sufficient to give a very good approximation of the bound states wavefunctions that improves with an increase in the basis size.
