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

Journal of Shaanxi Institute of Technology

Explanation of the polarized quantum in Zeeman effect

Yingli Pan

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

On the basis of the coherent state of quantum mechanics, this paper discusses the probability density of hydrogen atom without considering L-S interaction and points out that a hydrogen atom is an oscillating dipole if △m=0 and a rotation dipole if △m=±1 . Thus, it explains the causes of the polarized state in Zeeman effect in detail, gives a vivid physical picture and clarifies the vague concepts on the explanation of the polarized state in traditional text_books.

Related papers

Collective Spin Oscillations in Spin-Polarized Gases: Spin-Polarized Hydrogen

Laurent P. Lévy, Andrei E. Ruckenstein

The spin dynamics of weakly interacting, spin-polarized quantum gases are discussed in terms of a quasiparticle picture of these systems. Quantum mechanical exchange between identical particles introduces "molecular" magnetic fields which give rise to the precession of the spin current; this in turn leads to coherent oscillations of the magnetization. The theory is used to discuss magnetic resonance experiments in spin-polarized atomic hydrogen.

Physical Review Letters•Apr 23, 1984•87 citations

The probability density distribution and electric dipole moment of hydrogen atom in electric field

Gong Jian-pin

Using numerical method the picture of probability distribution of the electron in Stark effect is analyzed,the relationship between the direction of the electric dipole moment and the probability density distribution is also discussed.

College Physics•Jan 1, 2014•0 citations

The polarization properties of an atomic gas in a coherent state

Yu. M. Poluéktov

A possibility of polarization of the gas of hydrogen-like atoms at zero temperature in the Bose–Einstein condensate is studied at equilibrium and nonequilibrium conditions. The Gross–Pitaevskii equation is generalized for a gas of atoms considering their electronic structure. It is shown that the wave function of the system of interacting bosons in a single-particle condensate at zero temperature looks like the Glauber coherent state. With the help of the generalized Gross–Pitaevskii equation the polarization properties of atomic gas in the Bose–Einstein condensation state are investigated. It is shown that the electron stationary states in atoms of a gas in the coherent state differ from the electron stationary states in free atoms. Because of this the superfluid system can be spontaneously polarized, even if the free atoms in the stationary states have no intrinsic electric dipole moment. The polarization properties of a system of double-level hydrogen-like atoms in the Bose–Einstein condensate are studied more comprehensively. The propagation of both sound and high-frequency small disturbances in the coherent system of polarized atoms is accompanied by oscillations of polarization. The applicability of the developed idea to the analysis of electrical phenomena in superfluid helium is discussed.

Low Temperature Physics•Dec 1, 2011•10 citations

Exact Solution of the Zeeman Effect in Single-Electron Systems

A Blom

Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum-mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position of the plasma span the entire region from weak to strong fields, and there is a need for a unified treatment. In this paper we present the detailed quantum-mechanical derivation of the exact eigenenergies and eigenstates of hydrogen-like atoms and ions in a static magnetic field. Notably, these formulas are not much more complicated than the better-known approximations. Moreover, the derivation allows the value of the electron spin gyromagnetic ratio g s to be different from 2. For completeness, we then review the details of dipole transitions between two hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various approximations made in the derivation are also discussed in details.

arXiv:physics/0406141•Physica Scripta•Jan 1, 2005•4 citations

Polarization of Zeeman spectrum

Zhu Zhen-he

It is explained in detail how the σ polarization and π polarization of Zeeman spactrum are formed. The explanation is based on the fact that the quantum number of photon angular momentum is equal to 1 and the relation between the angular momentum of photon and the polarization of light.

College Physics•Jan 1, 2003•0 citations

Can the atomic spectra be explained by classical electromagnetic field theory

X. Q. Huang

We study the energy conversion laws of the macroscopic harmonic $LC$ oscillator, the electromagnetic wave (photon) and the hydrogen atom. As our analysis indicates that the energies of these apparently different systems obey exactly the same energy conversion law. Based on our results and the wave-particle duality of electron, we find that the atom in fact is a natural microscopic $LC$ oscillator. In the framework of classical electromagnetic field theory we analytically obtain, for the hydrogen atom, the quantized electron orbit radius $r_{n}=a_{0}n^{2}$, and quantized energy $E_{n}=-R_{H}hc/n^{2},$ ($n=1,2,3,...),$ where $a_{0}$ is Bohr radius and $R_{H}$ is Rydberg constant. Without any adaptation of the quantum theory, we present a reasonable explanation of the Zeeman effect, Selection rules and Pauli exclusion principle. Our results show that the concept of electron spin is not the physical reality and should be replaced by the intrinsic characteristic of the helical moving electron (Left-hand and Right-hand). In addition, a possible physical mechanism of superconductivity is also provided.

•Jan 21, 2006•0 citations
On the basis of the coherent state of quantum mechanics, this paper discusses the probability density of hydrogen atom without considering L-S interaction and points out that a hydrogen atom is an oscillating dipole if △m=0 and a rotation dipole if △m=±1 . Thus, it explains the causes of the polarized state in Zeeman effect in detail, gives a vivid physical picture and clarifies the vague concepts on the explanation of the polarized state in traditional text_books.
A possibility of polarization of the gas of hydrogen-like atoms at zero temperature in the Bose–Einstein condensate is studied at equilibrium and nonequilibrium conditions. The Gross–Pitaevskii equation is generalized for a gas of atoms considering their electronic structure. It is shown that the wave function of the system of interacting bosons in a single-particle condensate at zero temperature looks like the Glauber coherent state. With the help of the generalized Gross–Pitaevskii equation the polarization properties of atomic gas in the Bose–Einstein condensation state are investigated. It is shown that the electron stationary states in atoms of a gas in the coherent state differ from the electron stationary states in free atoms. Because of this the superfluid system can be spontaneously polarized, even if the free atoms in the stationary states have no intrinsic electric dipole moment. The polarization properties of a system of double-level hydrogen-like atoms in the Bose–Einstein condensate are studied more comprehensively. The propagation of both sound and high-frequency small disturbances in the coherent system of polarized atoms is accompanied by oscillations of polarization. The applicability of the developed idea to the analysis of electrical phenomena in superfluid helium is discussed.
Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum-mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position of the plasma span the entire region from weak to strong fields, and there is a need for a unified treatment. In this paper we present the detailed quantum-mechanical derivation of the exact eigenenergies and eigenstates of hydrogen-like atoms and ions in a static magnetic field. Notably, these formulas are not much more complicated than the better-known approximations. Moreover, the derivation allows the value of the electron spin gyromagnetic ratio g s to be different from 2. For completeness, we then review the details of dipole transitions between two hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various approximations made in the derivation are also discussed in details.
We study the energy conversion laws of the macroscopic harmonic LCLCLC oscillator, the electromagnetic wave (photon) and the hydrogen atom. As our analysis indicates that the energies of these apparently different systems obey exactly the same energy conversion law. Based on our results and the wave-particle duality of electron, we find that the atom in fact is a natural microscopic LCLCLC oscillator. In the framework of classical electromagnetic field theory we analytically obtain, for the hydrogen atom, the quantized electron orbit radius rn=a0n2r_{n}=a_{0}n^{2}rn​=a0​n2, and quantized energy En=−RHhc/n2,E_{n}=-R_{H}hc/n^{2},En​=−RH​hc/n2, (n=1,2,3,...),n=1,2,3,...),n=1,2,3,...), where a0a_{0}a0​ is Bohr radius and RHR_{H}RH​ is Rydberg constant. Without any adaptation of the quantum theory, we present a reasonable explanation of the Zeeman effect, Selection rules and Pauli exclusion principle. Our results show that the concept of electron spin is not the physical reality and should be replaced by the intrinsic characteristic of the helical moving electron (Left-hand and Right-hand). In addition, a possible physical mechanism of superconductivity is also provided.