Nonlinear Schrodinger equation and classical-field description of the Lamb-Retherford experiment

TL;DR

This paper demonstrates that the Lamb-Retherford experiment can be explained using classical field theory, deriving the stimulated decay rate of hydrogen's metastable state without quantum state concepts.

Contribution

It introduces a classical-field approach to describe the Lamb-Retherford experiment, avoiding quantum state and electron transition assumptions.

Findings

Derived the stimulated decay rate dependence on external field parameters.

Identified the maximum decay rate at frequencies matching fine structure or Lamb shift.

Showed classical field theory can replicate quantum experimental results.

Abstract

I show that Lamb-Retherford experiment can be fully described within the framework of classical field theory without using concepts such as the discrete states of the atom and jump-like electron transitions between them. The rate of stimulated decay of the metastable state of a hydrogen atom in an external periodic electric field is determined. The dependence of this rate on the frequency and amplitude of the external electric field, as well as on the parameters of the atom, has been obtained. It is shown that the maximum value of the stimulated decay rate of the metastable state of a hydrogen atom is achieved at an external electric field frequency equal to the frequency shift corresponding to either the fine structure of the hydrogen atom or the Lamb shift.