相对论性推广的类氢矩阵元的Blanchard递推关系
Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements
摘要：
在狄拉克相对论量子力学中导出了任意非对角径向类氢矩阵元的一般递推关系。我们的方法是基于以前在非相对论薛定谔的情况下采用的第二hypervirial方法的推广。由此得到对角情形（即总角动量和宇称相同）的Pasternack-Sternheimer关系的相对论形式，并由此导出相对论维里定理的表达式。为了有助于实用的关系，明确表达的径向矩阵元素的形式$r^λ$和$βr^λ$ -其中$β$是一个狄拉克矩阵的功能。
英文摘要：
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schrödinger case. A relativistic version of the Pasternack-Sternheimer relation is thence obtained in the diagonal (i.e. total angular momentum and parity the same) case, from such relation an expression for the relativistic virial theorem is deduced. To contribute to the utility of the relations, explicit expressions for the radial matrix elements of functions of the form $r^λ$ and $βr^λ$ ---where $β$ is a Dirac matrix--- are presented.
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