TL;DR
This paper explores how to formulate a Lorentz-covariant quantum description of the hydrogen atom, integrating concepts from relativity and quantum mechanics using harmonic oscillators to address the problem.
Contribution
It proposes a method to assemble quantum bound state descriptions of the hydrogen atom that are consistent with Lorentz covariance, utilizing harmonic oscillators.
Findings
A Lorentz-covariant quantum model of the hydrogen atom is feasible.
Harmonic oscillators can be used to construct Lorentz-invariant bound states.
The approach bridges quantum mechanics and special relativity for atomic systems.
Abstract
In 1905, Einstein formulated his special relativity for point particles. For those particles, his Lorentz covariance and energy-momentum relation are by now firmly established. How about the hydrogen atom? It is possible to perform Lorentz boosts on the proton assuming that it is a point particle. Then what happens to the electron orbit? The orbit could go through an elliptic deformation, but it is not possible to understand this problem without quantum mechanics, where the orbit is a standing wave leading to a localized probability distribution. Is this concept consistent with Einstein's Lorentz covariance? Dirac, Wigner, and Feynman contributed important building blocks for understanding this problem. The remaining problem is to assemble those blocks to construct a Lorentz-covariant picture of quantum bound states based on standing waves. It is shown possible to assemble those…
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Taxonomy
TopicsQuantum Mechanics and Applications · Experimental and Theoretical Physics Studies · Radioactive Decay and Measurement Techniques