  Here, we propose a new modified quantum mechanics and its new algorithms of
atomic fine-structure,asymmetric variational method based on hydrogen-like atom
orbit. In addition, as we all know, the ab initio calculation of atomic
fine-structure is the first driving force to create relativistic quantum
mechanics, so every new development of it is an interesting and important hot
topic. But we will not try to prove (or refute) strictly, because there is no
analytical solution to the multi-body Schrodinger equation and the magnetic
potential integral of ampere force of Langevin, so we use our method to
calculate the atom fine-structure of within the second period, and prove that
our calculation is closer to the experimental observation value through this
numerical experiment method (Our calculation accuracy is better than those of
relativistic Hartree-Fock method). Therefore, our discussion is a positive
exploration and conjecture.
