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Paper   IPM / Astronomy / 17276
School of Astronomy
  Title:   Departure to pure de Sitter geometry based on Planck data
1.  K. Suratgar
2.  M. Mohsenzadeh
3.  E. Yusofi
4.  F. Tagizadeh-Farahmand
  Status:   Published
  Journal: International Journal of Geometric Methods in Modern Physics
  No.:  09
  Vol.:  19
  Year:  2022
  Supported by:            ipm IPM
In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through the gnomonic projection and then quantize it in the standard way. We then recast the Hamiltonian in a shape-invariant form and derive the spectrum energy of the confined harmonic oscillator on the circle. With help of the f-deformed oscillator algebra, we construct the coherent states on the circle and investigate their quantum statistical properties. We find that such states show nonclassical features like squeezing and sub-Poissonian statistics even in small curvatures of the circle

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