The energy level structure of the modified Schrodinger equation can be consistent with Lamb shift

TL;DR

This paper proposes a modified Schrödinger equation that aligns with the Lamb shift in energy levels, offering a simpler alternative to complex QED calculations for atomic systems.

Contribution

It introduces a modified Schrödinger equation with a correction function that reproduces the Lamb shift, providing a new approach to atomic energy level calculations.

Findings

Modified Schrödinger equation matches Lamb shift in hydrogen-like systems

Demonstrates potential for simplified atomic energy calculations

Validates approach with helium-like systems

Abstract

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.