球对称弱引力场中Dirdc方程的非相对论近似及其能级

本文在球对称引力源的弱场近似中,写出Dirac方程,继之导出了它的非相对论近似的薛定谔方程。对出现在哈密顿量中的各项的物理意义作了讨论。特别由此可得到基本粒子自旋在引力场中的进动公式。最后还求出相应于哈密顿量的束缚态能级,表明在所设的近似条件下与氢原子的精细结构十分相似。

The Nonrelativistic Approximation of the Dirac Equation and I ts Energy Levels in the Weak Gravitational Field

In this paper we have written the Dirac. equation in static source of gravitation with weak field approximation at a spherically symmetrical case and then a nonrelativistic Schrodiger equation is derived. The physical meanings of every term appearing in the Hamiltonian are discussed. Especially from there we get the geodeti ic precession formula of a spin 1/2 ferrnion in the gravitational field. It is shown that the conduct of the spin of an elementary particle in the graritational field is the same as of a gyroscope. At last, the energy levels of the gravitational bond states are calculated. It is shown that under the conditions of the approximation we have put the energy levels are very similar to the fine structure of hydrogenir atoms.