Exact And Quasi — Exact Solvability of Second Order Superintegrable Quantum Systems
Exact And Quasi — Exact Solvability of Second Order Superintegrable Quantum Systems
复制标题
精确与拟——二阶超可积量子系统的精确可解性
DOI：
10.1007/978-0-387-73831-4_22
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Pogosyan
中科院分区：
文献类型：
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作者：
E. Kalnins;W. MillerJr.;G. Pogosyan
量子力学中的准精确可解（QES）问题是薛定谔算子的特征值问题，即使不存在完整特征值集的精确代数表达式，也可以精确计算一定数量的特征值和特征函数。过去，数学物理学家曾使用隐对称方法来解决这些问题。我们对这些方法进行了简要回顾，然后展示了超可积理论和变量分离所提供的对此类问题结构的深入了解。
Quasi-exactly solvable (QES) problems in quantum mechanics are eigenvalue problems for the Schrödinger operator where it is posssible to compute exactly a certain finite number of eigenvalues and eigenfunctions, even though exact algebraic expressions for the full set of eigenvalues do not exist. In the past, mathematical physicists have used hidden symmetry methods to attack these problems. We give a brief review of these methods and then show the increased insight into the structure of such problems provided by superintegrability theory and separation of variables.