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

Physical Review A

Nonspreading coherent states for the hydrogen atom

Bo-Wei Xu, Guo-Hui Ding, Kong Fan–mei

Published Jul 13, 2000• 4 citations
Publisher

Abstract

We construct the exact nonspreading coherent state for the Coulomb problem, the averaged motion of which describes a Kepler ellipse, and the coherent state around the average is a Guassian wave function. The obtained coherent state is expanded with respect to the bound eigenstates of the hydrogen atom in parabolic coordinates.
DOI
10.1103/physreva.62.022106

Related papers

Properties of Coherent State for Hydrogen Atom

Xu Bo-wei, Ye Fei, Guo-Hui Ding

We construct the coherent state for the two-dimensional hydrogen atom, for which the averaged motion of position describes a Kepler ellipse. The coherent state can be expanded with respect to the eigenstates of 2D hydrogen atom, from which we evaluate the binding energy of the wave packet for this state.

Communications in Theoretical Physics•Feb 15, 2003•2 citations

Propterties of Coherent State for Hydrogen Atom

XuBO-Wei, YEFei

We construct the coherent state for the two-dimensional hydrogen atom,for which the averaged motion of position describes a Kepler ellipse.The coherent state can be expanded with respect to the eigenstates of 2D hydrogen atom,from which we evaluate the binding energy of the wave packet for this state.

理论物理通讯:英文版•Jan 1, 2003•0 citations

KEPLER ORBITS FOLLOWED BY HYDROGEN ATOMS IN COHERENT STATES

Xu Bo-wei, GU WEI-HUA, 上海交通大学应用物理系,上海200030

Transforming the Coulomb problem to harmonic osillator, we construct nonspreading coherent states for the 2D and 3D hydrogen atom and show that the expectation values of the observables in Q. M. follow the classical Kepler orbits in physical space. The use of a fictitious time variable in the associated auxiliary osillator problem plays a crucial role.

Acta Physica Sinica•Jan 1, 1993•2 citations

Coherent states for the Kepler motion

Tadashi Toyoda, 澄子 若山

The dynamics of the electron wave function in a hydrogen atom is mapped onto that of a two-dimensional harmonic oscillator. Based on the harmonic-oscillator eigenstates, a coherent state wave function for the atomic electron is proposed.

Physical Review A•Feb 1, 1999•18 citations

Parametric time-coherent states for the hydrogen atom

Nuri Ünal

We obtained coherent states for the hydrogen atom by transforming the problem into four oscillators in the parametric time at a classical level, and quantizing these oscillators by using path integration over their holomorphic coordinates. We showed that for the negative- (positive-) energy coherent states the mean values of the physical position of the electron satisfy the Keplerian ellipses (hyperbolas) and that their dispersions oscillate (increase) in parametric time.

Physical Review A•Apr 16, 2001•13 citations

The Coherent States of the Hydrogen Atom

Didier Robert, Monique Combescure

The aim of this chapter is to present a construction of a set of coherent states for the hydrogen atom proposed by Villegas-Blas (The Laplacian on the n-sphere, the hydrogen atom and the Bargmann space representation. Ph.D. thesis, Mathematics Department, University of Virginia, 1996, [251]), Thomas and Villegas-Blas (Commun Math Phys 187:623–645, 1997, [244]). We show that in a semiclassical sense they concentrate essentially around the Kepler orbits (in configuration space) of the classical motion. A suitable unitary transformation (the Fock operator) maps the pure point subspace of the hydrogen atom Hamitonian onto the Hilbert space \(L^2({\mathbb S}^3)\) for the \(\mathbb S^3\) sphere. We study the coherent states for the \(\mathbb S^3\) sphere (as introduced by Uribe (J Funct Anal 59:535–556, 1984, [247]) and show that the action of the group SO(4) is irreducible in the space generated by the spherical harmonics of a given degree. Note that coherent states for the hydrogen atom have been extensively studied by J. Klauder and his school. We have chosen not to present them here and refer the interested reader to Klauder and Skagerstam (Coherent states, Worlds Scientific Publishing, Singapore, 1985, [167]).

Theoretical and mathematical physics•Jan 1, 2021•1 citation
The aim of this chapter is to present a construction of a set of coherent states for the hydrogen atom proposed by Villegas-Blas (The Laplacian on the n-sphere, the hydrogen atom and the Bargmann space representation. Ph.D. thesis, Mathematics Department, University of Virginia, 1996, [251]), Thomas and Villegas-Blas (Commun Math Phys 187:623–645, 1997, [244]). We show that in a semiclassical sense they concentrate essentially around the Kepler orbits (in configuration space) of the classical motion. A suitable unitary transformation (the Fock operator) maps the pure point subspace of the hydrogen atom Hamitonian onto the Hilbert space L2(S3)L^2({\mathbb S}^3)L2(S3) for the S3\mathbb S^3S3 sphere. We study the coherent states for the S3\mathbb S^3S3 sphere (as introduced by Uribe (J Funct Anal 59:535–556, 1984, [247]) and show that the action of the group SO(4) is irreducible in the space generated by the spherical harmonics of a given degree. Note that coherent states for the hydrogen atom have been extensively studied by J. Klauder and his school. We have chosen not to present them here and refer the interested reader to Klauder and Skagerstam (Coherent states, Worlds Scientific Publishing, Singapore, 1985, [167]).