相对论量子力学中矩阵元的计算
The Calculation of Matrix Elements in Relativistic Quantum Mechanics
摘要：
利用相对论性的超维里结果，最近在Dirac相对论性量子力学中得到了任意非对角径向类氢矩阵元的递推关系.在这方面的贡献，以表彰教授Löwdin，我们报告了一个新的关系，我们最近发现之间的矩阵元素$<2| r^λ|1 >$和$<2|βr^λ|1>$ -其中$β$是一个狄拉克矩阵和数字distiguish之间不同的径向本征态-这允许一个简化，因此为一个更方便的方式来表达递归关系。我们还导出了另一个关系，可以用来简化相对论原子或分子计算中的双中心矩阵元计算。
英文摘要：
Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring Professor Löwdin, we report on a new relation we have recently discovered between the matrix elements $<2| r^λ|1 >$ and $<2|βr^λ|1>$---where $β$ is a Dirac matrix and the numbers distiguish between different radial eigenstates--- that allow for a simplification and hence for a more convenient way of expressing the recurrence relations. We additionally derive another relation that can be employed for simplifying two center matrix element calculations in relativistic atomic or molecular calculations.
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