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2010•International Journal of Modern Physics AOpen access

GENERALIZED COHERENT STATES FOR THE SPHERICAL HARMONICS $Y_{m}^{m}(\theta,\phi)$

H. Fakhri, B. Mojaveri

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Abstract

The associated Legendre functions [Formula: see text] for a given l-m, may be taken into account as the increasing infinite sequences with respect to both indices l and m. This allows us to construct the exponential generating functions for them in two different methods by using Rodrigues formula. As an application then we present a scheme to construct generalized coherent states corresponding to the spherical harmonics [Formula: see text].

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The associated Legendre functions [Formula: see text] for a given l-m, may be taken into account as the increasing infinite sequences with respect to both indices l and m. This allows us to construct the exponential generating functions for them in two different methods by using Rodrigues formula. As an application then we present a scheme to construct generalized coherent states corresponding to the spherical harmonics [Formula: see text].

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Available abstract

The associated Legendre functions [Formula: see text] for a given l-m, may be taken into account as the increasing infinite sequences with respect to both indices l and m. This allows us to construct the exponential generating functions for them in two different methods by using Rodrigues formula. As an application then we present a scheme to construct generalized coherent states corresponding to the spherical harmonics [Formula: see text].

Key concepts: Physics, Spherical harmonics, Legendre function, Mathematical physics, Exponential function, Harmonics, Legendre polynomials, Coherent states

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