位置、动量和四维空间中旋量波函数和Slater型旋量轨道的二分量和四分量完全正交规范集的组合理论
Combined theory of two- and four- component complete orthonormal sets of spinor wave functions and Slater type spinor orbitals in position, momentum and four-dimensional spaces
摘要：
本文利用作者在前几篇文章中提出的非相对论标量轨道的完全标准正交基组，在位置、动量和四维空间中建立了用于准相对论和Dirac相对论方程描述自旋为1/2粒子的二分量和四分量旋量波函数以及Slater旋量轨道的新的完全标准正交基组。这些函数集通过相应的非相对论轨道来表示。本文还导出了位置空间中具有相同屏蔽常数的四分量相对论性Slater旋量轨道上重叠积分的解析公式。本文所得到的关系式可用于研究准相对论和相对论量子力学中位置、动量和四维空间的不同问题。
英文摘要：
By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two- and four-component spinor wave functions, and Slater spinor orbitals useful in the quantum-mechanical description of the spin- 1/2 particles by the quasirelativistic and Dirac's relativistic equations are established in position, momentum and four-dimensional spaces. These function sets are expressed through the corresponding nonrelativistic orbitals. The analytical formulas for overlap integrals over four-component relativistic Slater spinor orbitals with the same screening constants in position space are also derived. The relations obtained in this study can be useful in the study of different problems arising in the quasirelativistic and relativistic quantum mechanics when the position, momentum and four dimensional spaces are employed.
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