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| Paper IPM / P / 7615 |
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| Abstract: | |||||
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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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