Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Прикладная физика и математика.

QUASICLASSICAL INTERPRETATION OF ELECTRON S-STATE IN ATOM WITHIN THE FRAMEWORK OF RELATIVISTIC QUANTUM MECHANICS WITH ACCOUNT FOR MODELING OF CHARGE DISTRIBUTION INSIDE THE PROTON

А.П. ДАВЫДОВ, Tatiana Pavlovna Zlydneva

Published Oct 27, 2020• 0 citations
Publisher

Abstract

Используя результаты численного решения уравнения Дирака для электрона в 1S-состоянии в атоме водорода с учетом моделирования экспоненциального распределения заряда протона, уточняется предложенная ранее квазиклассическая интерпретация движения электрона вдоль радиальной линии непосредственно через ядро. Using the results of a numerical solution of the Dirac equation for an electron in the 1S state in a hydrogen atom, taking into account the modeling of the exponential distribution of the proton charge, the previously proposed quasiclassical interpretation of the motion of an electron along a radial line directly through the nucleus is refined.

DOI
10.25791/pfim.05.2020.1177

Related papers

CLASSICAL INTERPRETATION OF THE S-STATE OF AN ELECTRON IN ATOM FROM THE POINT OF VIEW OF THE QUANTUM MECHANICS QUASI-CLASSICAL APPROXIMATION

А.П. ДАВЫДОВ, Tatiana Pavlovna Zlydneva

На основе квазиклассического подхода в рамках квантовой механики предлагается классическая интерпретация движения электрона в атоме в его sсостоянии как движение по радиальным линиям с возможностью туннельного перехода сквозь ядро и изменением направления движения в результате столкновений с кварками ядра. Based on a quasiclassical approach within the framework of quantum mechanics, we propose a classical interpretation of the electron motion in an atom in its sstate as a motion along radial lines with the possibility of tunneling through the nucleus and changing the direction of motion as a result of collisions with the nuclei quarks.

Инженерная физика.•Jul 1, 2019•0 citations

Специфика взаимодействий в атоме водорода и зависимость скорости электрона и постоянной Планка от температуры

И. И. Чуев

A quantitative analysis of the forces acting between the electron and proton in a hydrogen atom, and given their theoretical justification. A new interpretation of the first Bohr's postulate. On the basis of this equation is obtained for calculating constant (quantum mechanical factor) Planck. Quantified and its dependence on the temperature and velocity of the electron. Evaluated the frequency of electron transitions and the value of the ionization energy of the hydrogen atom.

Universum•Jan 1, 2014•0 citations

Schrodinger equation solution for the hydrogen atom with consideration of nucleus rotation (spin)

В. И. Башков, D. Zenkin

The variant of the Schroedinger equation solution for the atom of hydrogen is submitted in view of the nucleus rotation, i.t. with the account received earlier by one of the authors potential energy for a rotating pointed charged particle. The received result allows by a quasi-classical way to take into account in the analytical decision of the Schroedinger equation for atom of hydrogen additional splitting of the atom energy levels because of rotation of the atomic nucleus.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 14, 2000•0 citations

The de Broglie-Bohm Causal Interpretation of Quantum Mechanics and its Application to some Simple Systems

Caroline Colijn

The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrödinger, Pauli and Dirac hydrogen eigenstates. In the Schrödinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schrödinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the z-axis. Electron trajectories are also found for the 1s-2p0 transition problem under the Schrödinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard quantum distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the standard distribution. Several promising avenues for future research are discussed.

•Jan 1, 2003•2 citations

О релятивистских поправках к энергии электрона в водородоподобном атоме

В. В. Скобелев

С использованием найденного в предыдущих работах разложением по малому параметру (Zα), α = е²/ħс ≈ 1/137 решения уравнения Дирака для электрона в поле ядра (Ze), выражающегося через собственную функцию оператора проектирования спина Σ₃, рассчитаны релятивистские и «спин-орбитальные» поправки к энергии электрона в водородоподобном атоме, причем последние, на наш взгляд, представлены в более наглядной по сравнению с ранее известными классическими результатами форме. Работа может представлять методический интерес в смысле некоторой модификации соответствующих разделов традиционного курса квантовой механики.

•Jan 1, 2017•0 citations

Движение электрона в почти кулоновском поле

Д. В. Калиновский, Е. С. Савин

will be added. One can explain the nature of the term by examining the relativistic case. Below the formulas for the radial and angular parts of the wave function were evaluated. The term for the energetic levels of the hydrogen atom for specific quantum numbers was given. We calculated the values of several specific radial functions for different quantum numbers, as well as the values of the radial function at the origin of coordinates and wide apart. A number of mean values for different powers of r was calculated. For the continuous spectrum the radial eigenfunctions were calculated.

Fine Chemical Technologies•Apr 28, 2013•0 citations
Используя результаты численного решения уравнения Дирака для электрона в 1S-состоянии в атоме водорода с учетом моделирования экспоненциального распределения заряда протона, уточняется предложенная ранее квазиклассическая интерпретация движения электрона вдоль радиальной линии непосредственно через ядро. Using the results of a numerical solution of the Dirac equation for an electron in the 1S state in a hydrogen atom, taking into account the modeling of the exponential distribution of the proton charge, the previously proposed quasiclassical interpretation of the motion of an electron along a radial line directly through the nucleus is refined.
На основе квазиклассического подхода в рамках квантовой механики предлагается классическая интерпретация движения электрона в атоме в его sсостоянии как движение по радиальным линиям с возможностью туннельного перехода сквозь ядро и изменением направления движения в результате столкновений с кварками ядра. Based on a quasiclassical approach within the framework of quantum mechanics, we propose a classical interpretation of the electron motion in an atom in its sstate as a motion along radial lines with the possibility of tunneling through the nucleus and changing the direction of motion as a result of collisions with the nuclei quarks.
The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrödinger, Pauli and Dirac hydrogen eigenstates. In the Schrödinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schrödinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the z-axis. Electron trajectories are also found for the 1s-2p0 transition problem under the Schrödinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard quantum distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the standard distribution. Several promising avenues for future research are discussed.
С использованием найденного в предыдущих работах разложением по малому параметру (Zα), α = е²/ħс ≈ 1/137 решения уравнения Дирака для электрона в поле ядра (Ze), выражающегося через собственную функцию оператора проектирования спина Σ₃, рассчитаны релятивистские и «спин-орбитальные» поправки к энергии электрона в водородоподобном атоме, причем последние, на наш взгляд, представлены в более наглядной по сравнению с ранее известными классическими результатами форме. Работа может представлять методический интерес в смысле некоторой модификации соответствующих разделов традиционного курса квантовой механики.
will be added. One can explain the nature of the term by examining the relativistic case. Below the formulas for the radial and angular parts of the wave function were evaluated. The term for the energetic levels of the hydrogen atom for specific quantum numbers was given. We calculated the values of several specific radial functions for different quantum numbers, as well as the values of the radial function at the origin of coordinates and wide apart. A number of mean values for different powers of r was calculated. For the continuous spectrum the radial eigenfunctions were calculated.