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      Quantum stereographic projection and the homographic oscillator

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      Author(s)
      Hakioǧlu T.
      Arik, M.
      Date
      1996
      Source Title
      Physical Review A - Atomic, Molecular, and Optical Physics
      Print ISSN
      1050-2947
      Publisher
      American Physical Society
      Volume
      54
      Issue
      1
      Pages
      52 - 56
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      The quantum deformation created by the stenographic mapping from S2 to C is studied. It is shown that the resulting algebra is locally isomorphic to su(2) and is an unconventional deformation of which the undeformed limit is a contraction onto the harmonic oscillator algebra. The deformation parameter is given naturally by the central invariant of the embedding su(2). The deformed algebra is identified as a member of a larger class of quartic q oscillators. We next study the deformations in the corresponding Jordan-Schwinger representation of two independent deformed oscillators and solve for the deforming transformation. The invertibility of this transformation guarantees an implicit coproduct law which is also discussed. Finally we discuss the analogy between Poincaré's geometric interpretation of the quantum Stokes parameters of polarization and the stereographic projection as an important physical application of the latter.
      Keywords
      Algebra
      Eigenvalues and eigenfunctions
      Invariance
      Iterative methods
      Mathematical operators
      Mathematical transformations
      Nonlinear equations
      Coproduct law
      Fibonacci series
      Homographic oscillators
      Poincare geometry
      Quantum stereographic projection
      Quantum Stokes parameters
      Quantum theory
      Permalink
      http://hdl.handle.net/11693/25717
      Published Version (Please cite this version)
      https://doi.org/10.1103/PhysRevA.54.52
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      • Department of Physics 2397
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