An algebraic approach to problems with polynomial hamiltonians on euclidean spaces
An algebraic approach to problems with polynomial hamiltonians on euclidean spaces
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DOI：
10.1088/0305-4470/38/47/009
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发表时间：
2005-10
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影响因子：
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通讯作者：
D. Rowe
中科院分区：
文献类型：
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作者：
D. Rowe
给出了酉SU（1，1）表示的连续正交基序列中多维空间上基本径向观测量的作用量和径向矩阵元的显式表达式。给出了基本轨道观测量SO（N）约化矩阵元的显式表达式。这些发展使得有可能确定多项式的矩阵元素和其他哈密尔顿分析，在SO（N）Clebsch-Gordan系数，并选择一个最佳的基础，为一个特定的问题，使本征函数的扩展是最迅速收敛。
Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1, 1) irreps. Explicit expressions are also given for SO(N)-reduced matrix elements of basic orbital observables. These developments make it possible to determine the matrix elements of polynomial and other Hamiltonians analytically, to within SO(N) Clebsch–Gordan coefficients, and to select an optimal basis for a particular problem such that the expansion of eigenfunctions is most rapidly convergent.