The quantum states for Hydrogen atom: spherical harmonics and the orbitals geometrical representation

Q2 Engineering

INCAS Bulletin Pub Date : 2024-03-11 DOI:10.13111/2066-8201.2024.16.1.3

D. Constantin, L. Preda, A. A. Mocanu, D. Popescu, D. Pricopi, V. I. Niculescu

引用次数: 0

Abstract

Our work utilizes the quantum model of the hydrogen atom which is based on the Schrödinger equation with Coulomb potential. Specifically, we concentrate on the angular components of the wave eigenfunctions derived from this model. We consider the quantum states with n ≤ 4. In order to visualize the orbital shapes of these states, we built in the spherical coordinates system their 3D geometric representations. Furthermore, we use the corresponding spherical harmonics, to calculate the θ nodal values that describe the configurations of these orbital states.

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氢原子的量子态：球谐波和轨道几何表示法

我们的研究利用了基于库仑势的薛定谔方程的氢原子量子模型。具体来说，我们专注于从该模型推导出的波特征函数的角分量。我们考虑 n ≤ 4 的量子态。为了直观地显示这些状态的轨道形状，我们在球坐标系中建立了它们的三维几何表示。此外，我们还利用相应的球面谐波来计算描述这些轨道态构型的 θ 节点值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

INCAS Bulletin Engineering-Aerospace Engineering

自引率

0.00%

发文量

审稿时长

8 weeks

期刊介绍： INCAS BULLETIN is a scientific quartely journal published by INCAS – National Institute for Aerospace Research “Elie Carafoli” (under the aegis of The Romanian Academy) Its current focus is the aerospace field, covering fluid mechanics, aerodynamics, flight theory, aeroelasticity, structures, applied control, mechatronics, experimental aerodynamics, computational methods. All submitted papers are peer-reviewed. The journal will publish reports and short research original papers of substance. Unique features distinguishing this journal: R & D reports in aerospace sciences in Romania The INCAS BULLETIN of the National Institute for Aerospace Research "Elie Carafoli" includes the following sections: 1) FULL PAPERS. -Strength of materials, elasticity, plasticity, aeroelasticity, static and dynamic analysis of structures, vibrations and impact. -Systems, mechatronics and control in aerospace. -Materials and tribology. -Kinematics and dynamics of mechanisms, friction, lubrication. -Measurement technique. -Aeroacoustics, ventilation, wind motors. -Management in Aerospace Activities. 2) TECHNICAL-SCIENTIFIC NOTES and REPORTS. Includes: case studies, technical-scientific notes and reports on published areas. 3) INCAS NEWS. Promote and emphasise INCAS technical base and achievements. 4) BOOK REVIEWS.