相对论薛定谔理论中的正电子素基态
Positronium Groundstate in Relativistic Schroedinger Theory
摘要：
相对论性薛定谔理论（英语：Relativistic Schrödinger Theory）是在原子物理学领域研究的。作为一个具体的证明，我们详细地考虑了正电子素基态，特别是在非相对论近似下，在忽略正电子和电子之间的磁相互作用的情况下，计算了基态能量$E_0$，相应的非相对论性预测$(E_0\simeq -6,48 [eV])$与类似的传统薛定谔结果$(E_0\simeq -6,80 [eV])$不一致，但比相应的Hartree近似$(-2,65 [eV])$更接近后者. $6,80-6,48=0,32 [eV]$的结合能丢失可以归因于近似使用SO（3）对称相互作用势，然而，在量子力学中，实际上只有SO（2）对围绕z轴的旋转不变。可以预期的是，由于SO（2）对称性，正确使用各向异性相互作用势，量子力学的预测将更接近传统的薛定谔结果，然而量子力学的数学结构依赖于奇异（即双值）波函数和相应的非常规相互作用势（例如Struve-Neumann势）。
英文摘要：
The usefulness of the Relativistic Schrödinger Theory (RST) is studied in the field of atomic physics. As a concrete demonstration, the positronium groundstate is considered in great detail; especially the groundstate energy $E_0$ is worked out in the non-relativistic approximation and under neglection of the magnetic interactions between the positron and the electron. The corresponding RST prediction $(E_0\simeq -6,48 [eV])$ misses the analogous conventional Schrödinger result $(E_0\simeq -6,80 [eV])$ but is closer to the latter than the corresponding Hartree approximation $(-2,65 [eV])$. The missing binding energy of $6,80-6,48=0,32 [eV]$ can be attributed to the approximative use of an SO(3) symmetric interaction potential which in RST, however, is actually only SO(2) invariant against rotations around the z-axis. It is expected that, with the correct use of an anisotropic interaction potential due to the SO(2) symmetry, the RST predictions will come even closer to the conventional Schrödinger result, where however the mathematical structure of RST relies on exotic (i.e. double-valued) wave functions and on the corresponding unconventional interaction potentials (e.g. Struve-Neumann potential).
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