A new set of coherent states for the isotropic harmonic oscillator: Coherent angular momentum states

Bracken A.J. and Leemon H.I. (1980) A new set of coherent states for the isotropic harmonic oscillator: Coherent angular momentum states. Journal of Mathematical Physics, 22 4: 719-732. doi:10.1063/1.524964

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Author Bracken A.J.
Leemon H.I.
Title A new set of coherent states for the isotropic harmonic oscillator: Coherent angular momentum states
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
Publication date 1980-01-01
Sub-type Article (original research)
DOI 10.1063/1.524964
Open Access Status File (Publisher version)
Volume 22
Issue 4
Start page 719
End page 732
Total pages 14
Subject 1605 Policy and Administration
Abstract The Hamiltonian for the oscillator has earlier been written in the form H=ℏω(2v+v+λ+·λ+3/2), where v+ and v are raising and lowering operators for v+v, which has eigenvalues k (the "radial" quantum number), and λ+ and λ are raising and lowering 3-vector operators for λ+·λ, which has eigenvalues l (the total angular momentum quantum number). A new set of coherent states for the oscillator is now denned by diagonalizing v and λ. These states bear a similar relation to the commuting operators H, L2, and L3 (where L is the angular momentum of the system) as the usual coherent states do to the commuting number operators N1, N2, and N 3. It is proposed to call them coherent angular momentum states. They are shown to be minimum-uncertainty states for the variables v, v +λ, and λ+ and to provide a new quasiclassical description of the oscillator. This description coincides with that provided by the usual coherent states only in the special case that the corresponding classical motion is circular, rather than elliptical; and, in general, the uncertainty in the angular momentum of the system is smaller in the new description. The probabilities of obtaining particular values for k and l in one of the new states follow independent Poisson distributions. The new states are overcomplete, and lead to a new representation of the Hilbert space for the oscillator, in terms of analytic functions on C×K3, where K3 is the three-dimensional complex cone. This space is related to one introduced recently by Bargmann and Todorov, and carries a very simple realization of all the representations of the rotation group.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import - Archived
 
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