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Paper   IPM / Physic / 7615
School of Physics
  Title:   Barut-Girardello Coherent States Constructed by Ym m(θ,φ) and Ym+1m(θ,φ) for a Free Particle on the Sphere
1.  A. Chenaghlou
2.  H. Fakhri
  Status:   Published
  Journal: Mod. Phys. Lett. A
  No.:  35
  Vol.:  19
  Year:  2004
  Pages:   2619-2628
  Supported by:  IPM
Using the realization idea of simultaneous shape invariance with respect to two different parameters of the associated Legendre functions, the Hilbert space of spherical harmonics Yn m(θ,φ) corresponding to the motion of a free particle on a sphere is splitted into a direct sum of infinite dimensional Hilbert subspaces. It is shown that these Hilbert subspace constitute irreducible representations for the Lie algebra u(1,1). Then by applying the lowering operator of the Lie algebra u(1,1), Barut-Girardello coherent states are constructed for the Hilbert subspaces consisting of Ym m(θ,φ) and Ym+1 m (θ,φ).

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