Coherent states for the hydrogen atom

@article{Klauder1996CoherentSF,
  title={Coherent states for the hydrogen atom},
  author={John Klauder},
  journal={Journal of Physics A},
  year={1996},
  volume={29}
}
  • J. Klauder
  • Published 1996
  • Physics
  • Journal of Physics A
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 parametrized 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. 
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References

SHOWING 1-10 OF 21 REFERENCES
Possibility that Schrödinger's conjecture for the hydrogen-atom coherent states is not attainable.
  • Zlatev, Zhang, Feng
  • Physics, Medicine
  • Physical review. A, Atomic, molecular, and optical physics
  • 1994
TLDR
The most general SO(4,2) hydrogen atom coherent states are constructed which are the counterpart of Schr\"{o}dinger's harmonic oscillator coherent states and it is shown that these states cannot be localized and cannot follow the classical orbits. Expand
Classical Limit of the Hydrogen Atom
A wavepacket solution for the hydrogen atom in the region of large principal quantum number n is constructed. This wavepacket follows a classical circular orbit. It has a width on the order of n−1/2Expand
Classical and quantum-mechanical dynamics of a quasiclassical state of the hydrogen atom.
We explore the classical limit of the hydrogen atom by constructing a minimum-uncertainty wave packet that travels along a Kepler orbit. The dynamics of the wave packet display both classical andExpand
On the classical limit of the Kepler problem
We introduce coherent states on the dynamical group of the nonrelativistic Kepler (hydrogen atom) problem. In the limit of high excitation these states are well concentrated wavepackets which moveExpand
Atomic quantum states with maximum localization on classical elliptical orbits.
TLDR
These elliptic states are uniquely defined from symmetry considerations and are the coherent states of the SO(4) symmetry group of the Coulomb interaction in three dimensions and are superpositions of the usual spherical states with well-defined weights and phases. Expand
Generalized Coherent States and Their Applications
I Generalized Coherent States for the Simplest Lie Groups.- 1. Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom.- 1.1 The Heisenberg-Weyl Group and ItsExpand
COHERENT STATES WITHOUT GROUPS: QUANTIZATION ON NONHOMOGENEOUS MANIFOLDS
A wide class of single-variable holomorphic representation spaces are constructed that are associated with very general sets of coherent states defined without the use of transitively acting groups.Expand
Proceedings of the International Symposium, Coherent States : Past, Present, and Future, Oak Ridge Nat'l Lab 14-17 June 1993
The book consists of written versions of lectures delivered at the International Symposium on Coherent States: Past, Present and Future, held in Oak Ridge, Tennessee, June 14-17, 1993. BothExpand
Quantum wave packets on Kepler elliptic orbits.
  • Nauenberg
  • Physics, Medicine
  • Physical review. A, General physics
  • 1989
Wave-packet solutions of the Schr\"odinger equation for the Coulomb potential are obtained that travel along classical elliptic orbits of fixed mean eccentricity and angular momentum. These waveExpand
Quantization Without Quantization
Appropriate to a single classical degree of freedom, completely general, two-parameter ``coherent states`` are defined without the use of any group or any {ital c}-number to {ital q}-numberExpand
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