  In the literature of calculating atomic and molecular structures, most
Schrodinger equations are described by Coulomb potential. However, there are
also a few literatures that discuss some magnetic correction methods, such as
Pauli and Shortley's early work. But in fact, the calculation accuracy of these
Schrodinger equations is not consistent with Lamb shift. Therefore, in the
traditional ab initio calculation of quantum mechanics, it is common and
necessary to use Dirac theory or quantum electrodynamics (QED) to correct the
energy level of Schrodinger equation. However, the calculation of Feynman
diagram is a daunting problem, including the application of self-consistent
field in relativity and density functional theory. So recently, we have noticed
the simplicity of the modified Newtonian mechanics, and we think that quantum
mechanics will have similar properties. Here, we state this and improve the
correction function in our previous action potential. In addition, through the
demonstration of hydrogen-like and helium-like systems here, it can be proved
that this conclusion is a potential application, that is, the energy level
structure of our modified Schrodinger equation is consistent with Lamb shift.
