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General Many-Body Systems

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Hyperspherical Harmonics Expansion Techniques

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Abstract

Hyperspherical harmonics expansion method is generalized from three-body to A-body system, defining N Jacobi vectors and 3N hyperspherical variables for the relative motion, where \(N=A-1\). Analytic expression is derived for the generalized hyperspherical harmonics as the eigenfunction of the generalized hyperangular momentum operator. The kinematic rotation vector (KRV) is defined as a linear combination of the Jacobi vectors. Position vector of a particle from the center of mass and relative separation of a pair can be expressed as KRVs in terms of two sets of parametric angles. Procedure for symmetrization (including mixed symmetry) of the spatial wave function using KRV is described. It is emphasized that truncation of the basis is necessary for a practical calculation. Truncation schemes like restricting the symmetry component, retaining only the lowest hyperangular momentun (\(L_m\) approximation), restriction to optimal subset and the subset of potential harmonics have been introduced. Application of the truncation schemes to problems in particle, nuclear, and atomic physics has been discussed.

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  1. Department of Physics, University of Calcutta, Kolkata, West Bengal, India

    Tapan Kumar Das

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Das, T.K. (2016). General Many-Body Systems. In: Hyperspherical Harmonics Expansion Techniques. Theoretical and Mathematical Physics. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2361-0_4

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  • DOI: https://doi.org/10.1007/978-81-322-2361-0_4

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  • Print ISBN: 978-81-322-2360-3

  • Online ISBN: 978-81-322-2361-0

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