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

Coherent states for the Kepler motion

Tadashi Toyoda, 澄子 若山

Published Feb 1, 1999• 18 citations
Publisher

Abstract

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.
DOI
10.1103/physreva.59.1021

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

Nonspreading coherent states for the hydrogen atom

Bo-Wei Xu, Guo-Hui Ding, Kong Fan–mei

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.

Physical Review A•Jul 13, 2000•4 citations

Coherent States for the Hydrogen Atom

John R. Klauder

The long-standing problem of finding coherent states for the (bound state portion of the) hydrogen atom is positively resolved. The states in question: (i) are normalized and parameterized continuously, (ii) admit a resolution of unity with a positive measure, and (iii) enjoy the property that the temporal evolution of any coherent state by the hydrogen atom Hamiltonian remains a coherent state for all time. Harmonic-oscillator coherent states In modern terms, the distinguished set of states Schrodinger introduced for the harmonic oscillator 1 are now commonly known as coherent states 2 and are given, for all z 2 I C, by jzi j e (za y \\Gammaz a) j0i = e \\Gamma 1 2 jzj 2 1 X n=0 z n p n! jni; (1) where [a; a y ] = 1 as usual. Here jni; n = 0; 1; 2; : : :, denote normalized eigenstates of the number operator N , N jni = njni, which may be identified with the eigenstates of the harmonic oscillator Hamiltonian H 0 = !N = !a y a (¯h = 1). As such it follows that ...

•Nov 23, 1995•105 citations

ENERGY AND WAVE FUNCTION OF THE TWO DIMENSIONAL HARMONIC OSCILLTOR AND HYDROGEN ATOM

Hao Chen

By the coordinates counterchange,the relationship between energy and wave function of Two dimensional Harmonic Oscillator and Hydrogen Atom are found.

Journal of South China Normal University•Jan 1, 2004•0 citations

Wave Functions of Atomic Elliptic States

C Lena, Dominique Delande, J. C. Gay

The elliptic eigenstates of the hydrogen atom are the quantum analogs of the classical trajectories of the electron around the nucleus in the sense that they have the best transverse localization compatible with the uncertainty relations. The equivalence of the hydrogen atom with a harmonic oscillator provides us with a realization of the symmetry group and allows for the analytical study of the elliptic states. In particular we derive the 2D and 3D wave functions in a simple closed form.

Europhysics Letters (EPL)•Aug 1, 1991•30 citations
The long-standing problem of finding coherent states for the (bound state portion of the) hydrogen atom is positively resolved. The states in question: (i) are normalized and parameterized continuously, (ii) admit a resolution of unity with a positive measure, and (iii) enjoy the property that the temporal evolution of any coherent state by the hydrogen atom Hamiltonian remains a coherent state for all time. Harmonic-oscillator coherent states In modern terms, the distinguished set of states Schrodinger introduced for the harmonic oscillator 1 are now commonly known as coherent states 2 and are given, for all z 2 I C, by jzi j e (za y \\Gammaz a) j0i = e \\Gamma 1 2 jzj 2 1 X n=0 z n p n! jni; (1) where [a; a y ] = 1 as usual. Here jni; n = 0; 1; 2; : : :, denote normalized eigenstates of the number operator N , N jni = njni, which may be identified with the eigenstates of the harmonic oscillator Hamiltonian H 0 = !N = !a y a (¯h = 1). As such it follows that ...