Hydrogen atom as test field of theoretical models

Sergey A. Rashkovskiy

Abhijit Biswas, Krishnan R. S. Mani

Wei Feng

This study conducted a detailed study on the wave function characteristics of the hydrogen atom model and explored its potential applications in quantum computing, atomic spectral analysis and quantum information processing based on the Schrödinger equation. By solving the Schrödinger equation of the hydrogen atom, the form of the wave function was clearly obtained, and the distribution law of electrons at various energy levels was demonstrated. The study constructed a quantum theoretical model of the hydrogen atom, derived the regulatory effect of quantum numbers on the wave function, and solved the Schrödinger equation with the help of numerical analysis technology to ensure the accuracy and robustness of the wave function evaluation. The study conducted a detailed analysis of the energy level, wave function profile and electron probability density distribution of the hydrogen atom. The simulation results show that with the increase of energy level, the oscillation frequency of the wave function increases significantly, and the distribution space of electrons also expands accordingly. In addition, this study also explored the practical application of the hydrogen atom model. In the field of quantum computing, the wave function characteristics provide theoretical support for the initialization and manipulation of quantum bits; in atomic spectral analysis, accurately calculated energy levels and wave functions help to improve the accuracy of spectral measurement; in quantum information processing, the simulation of quantum entangled networks based on the hydrogen atom model provides new ideas for quantum communication and quantum computing. These applications demonstrate that the hydrogen atom model is not only of great significance in theoretical physics, but also has broad application prospects in emerging technology fields.

Yurii L. Sokolov

Matej Hrmo, Samuel Kováčik, Patrik Rusnák +1 more

The fuzzy onion model formed by connecting a set of concentric fuzzy spheres of increasing radius is motivated by studies of quantum space but can also be used to study standard physics. The main feature of the model is that functions in three-dimensional space—like scalar fields or wave functions—are expressed in terms of Hermitian matrices of a certain structure. Relevant equations are then matrix equations, and some problems, such as searching for the energy spectrum for fixed quantum numbers ( l , m ) , can be expressed as an eigenvalue problem. We show how this simple approach can reproduce the results of other studies analyzing the hydrogen atom in a spherical cavity. We also test the effect of the short-distance quantum structure of the space on these solutions—not looking for the phenomenological consequences, as the scale of quantum space is many orders below the order of the Bohr radius, but to understand the effect of quantum space in general. We observe a set of solutions without a classical counterpart which have been suggested also in a former theoretical study.

Andrés Felipe Ortiz, Snehanshu Saha