Coherent states for the hydrogen atom: discrete and continuous spectra

Details Coherent states for the hydrogen atom: discrete and continuous spectra Coherent states for the hydrogen atom: discrete and continuous spectra

2001-08-09

arxiv.org/abs/quant-ph/0108042v4

J.Phys.A 34 (2001) 11083

Physics

Quantum Physics

15 pages, LATEX, minor sign corrections, to appear in J.Phys.A

Scientific paper

10.1088/0305-4470/34/49/323

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group $SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular cases of the kernel of integral operator which interwines irreducible representations of the $SO(4, 2)$ group.

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