A Version of de Broglie’s Double Solution Theory Reproducing Landau’s Quantization in a Uniform Magnetic Field

Following the recent development of a mechanical atomic model based on Louis de Broglie’s double solution theory, we show how it is possible to obtain the famous Landau quantization rules for a purely classical electron coupled to a wave. We present both a qualitative but intuitive explanation of our model of wave-particle duality, as well as a more rigorous derivation of the solutions. This work completes a set of three articles, each using a different combination of external electric and magnetic forces on the same base model. Despite this similarity with previous approaches, it also uncovers some unique properties of this system. We will see that, in order to correctly recover some useful non-relativistic limits, it is necessary to use a scalar field whose mass is the same as an effective mass for the particle that naturally appears in our model. This could be a crucial step to better characterize the necessary ingredients of a double solution theory.