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Predictive Modeling of Quantum Beating in Hydrogen Atom:
Classical and Quantum Visualizations of Coherent State Dynamics (Fundamentals).

This work presents modeling results and prediction of the quantum beating effect in the attosecond time range. The process speed has been proportionally reduced to enable visual observation of electron transitions between states. The fundamental principles do not contradict non-relativistic quantum mechanics and are indirectly supported by its framework. While the exact density movies of the 1s–2p$_z$ beating are not yet directly measured, the underlying frequency scales and coherence phenomena are in close agreement with experimental evidence from ultrafast spectroscopy, Rydberg dynamics, and attosecond experiments.

mshell is a minimalistic Unix shell designed for resource-constrained environments, combining traditional shell functionality with integrated AI capabilities through local LLM models via Ollama or Linux LLM evaluation framework (current version of mshell is 1.4.1), cloud LLMs.
The most convenient way to do this is working in two stages. In the first stage, use the latex1.ms script (if the information sources are local) or the latex1inter.ms script (if the information sources are publicly available online). In the second stage, use the latex2.ms script to aggregate and format the article. Information sources can include images, TeX formulas, PDF files, flat files of various formats, and formula descriptions. You can find examples of scripts at the end of the PDF file.