Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法

Bound state solutions of the Dirac equation with the Makarov potentials

The bound state solutions of the Dirac equation with equal scalar and vector Makarov potentials are obtained. It is shown that angular component of the Dirac equation can be solved with the factorization method, which enables us to find immediately the eigenvalues and at the same time the manipulation process for the normalized eigenfunctions. The radial bound state solutions are expressed in terms of the confluent hypergeometric functions and the energy equation is derived from the boundary condition satisfied by the radial wavefunctions.