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

Acta Physica Sinica

DOUBLE-WAVE DESCRIPTION OF ONE-DIMENSIONAL HYDROGEN ATOM

HUANG XIANG-YOU, WANG JI-YE, YE XUE-MIN, 北京大学物理系，北京 100871

Published Jan 1, 1999• 0 citations
Publisher

Abstract

Stationary solutions of one-dimensional hydrogen atom are two-degree degenerate. Three kinds of typical solutions can be constructed from those degenerated solutions. They correspond to three kinds of ensembles. Double-wave theory describes a single hydrogen atom. When three different averages over ensembles are made for double-wave theory, three kinds of typical solutions in the usual quantum mechanics are obtained. A comparison between these solutions and those of classical mechanics is made.

DOI
10.7498/aps.48.566

Related papers

DOUBLE-WAVE DESCRIPTION OF A TWO-DIMENSIONAL HYDROGEN ATOM

C Huang

Double wave quantum theory is applied to the description of a two dimensional hydrogen atom.The classical limit of this description is discussed.The results indicate that double wave function can be applied to describe the states of single particle,and the ordinary quantum mechanical description,as a statistical average of ensemble,is included in the double wave quantum theory.

Acta Physica Sinica•Jan 1, 2000•0 citations

Double-Wave Description of a Three-Dimensional Hydrogen Atom and a Three-Dimensional Similar Hydrogen Atom

Ma Ai-Qun

In this paper, double-wave quantum theory is applied to describe a thr ee-dimensional hydrogen atom and a three-dimensional similar hydrogen atom, the classical limit of this description is discussed. It is proved that double-wave function satisfies the normalization condition. Under the description of double- wav e functions, the expectation value of energy and angular momentum are E n a nd m, respectively. A t the same time, we calculated the average values of r, cos θ, sin θ , cos φ, sin φ and X, Y, Z, under the description of double-wave fu nction. The statistical average va lue for mechanics quantity  shows that single-wave function describes the states of the system of hydrogen atom and similar hydrogen atom. Only double-wave func tion can describe the states of single microcosmic body.

Acta Sinica Quantum Optica•Jan 1, 2003•0 citations

Theory of Quantum Phase Space and Rigorous Solution of Hydrogen Atom

Jun Lu

The method of wave mechanics in the quantum phase-space representation established by TorresVega and Frederick is introduced.The Fourier-like projection transformation between phase-space representation and position or momentum representation is discussed.The rigorous solutions of stationary Schrdinger equation for one-dimensional hydrogen atom are obtained.It is described that the wave functions are not unique in phase space.

Journal of Hebei Normal University•Jan 1, 2007•0 citations

Wave mechanics in quantum phase space: hydrogen atom

Jun Lu

The rigorous solutions of the stationary Schrodinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The Fourier-like projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.

Progress in Natural Science Materials International•Feb 1, 2007•0 citations

ANALYSIS OF WAVE FUNCTIONS FOR HYDROGEN ATOMS IN CLASSICAL LIMIT

HUANG XIANG-YOU, 北京大学物理系,北京,100871;中国高等科学技术中心(世界实验室)

Basing on the classical trajectory motion for an electron circling an atomic nucleus and averaging the motion over initial coordinate parameters of ellipse trajectories for the electron, we get a density distribution in space. This distribution is consistent with probability density of stationary state for hydrogen atom in the classical limit. This comparison shows that a wave function of hydrogen atom in stationary state does not describe an individual atom but an ensemble.

Acta Physica Sinica•Jan 1, 1991•1 citation

Permanent Electric Dipole Moment of Hydrogen Atom

Weimin Du

The permanent electric dipole moment (PEDM) of hydrogen atom is calculated in classical mechanics and double-wave mechanics. The result of double-wave mechanics accords with the other result in classical limit. Because one wavefunction only describes an ensemble, the explanation to PEDM of hydrogen atom in orthodox quantum theory is difficult and unnatural. The classical mechanics and double-wave quantum mechanics could definitively describe single particle's action, and the calculations and explanations to PEDM in these two theories are more natural and reasonable.

Acta Sinica Quantum Optica•Jan 1, 2004•0 citations
Stationary solutions of one-dimensional hydrogen atom are two-degree degenerate. Three kinds of typical solutions can be constructed from those degenerated solutions. They correspond to three kinds of ensembles. Double-wave theory describes a single hydrogen atom. When three different averages over ensembles are made for double-wave theory, three kinds of typical solutions in the usual quantum mechanics are obtained. A comparison between these solutions and those of classical mechanics is made.
In this paper, double-wave quantum theory is applied to describe a thr ee-dimensional hydrogen atom and a three-dimensional similar hydrogen atom, the classical limit of this description is discussed. It is proved that double-wave function satisfies the normalization condition. Under the description of double- wav e functions, the expectation value of energy and angular momentum are E n a nd m, respectively. A t the same time, we calculated the average values of r, cos θ, sin θ , cos φ, sin φ and X, Y, Z, under the description of double-wave fu nction. The statistical average va lue for mechanics quantity  shows that single-wave function describes the states of the system of hydrogen atom and similar hydrogen atom. Only double-wave func tion can describe the states of single microcosmic body.
The rigorous solutions of the stationary Schrodinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The Fourier-like projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.
The permanent electric dipole moment (PEDM) of hydrogen atom is calculated in classical mechanics and double-wave mechanics. The result of double-wave mechanics accords with the other result in classical limit. Because one wavefunction only describes an ensemble, the explanation to PEDM of hydrogen atom in orthodox quantum theory is difficult and unnatural. The classical mechanics and double-wave quantum mechanics could definitively describe single particle's action, and the calculations and explanations to PEDM in these two theories are more natural and reasonable.