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The hyperspherical expansion method

  • M. Fabre de la Ripelle
Part II - Integral and Differential Methods for the Solution of the Schrödinger Equation
Part of the Lecture Notes in Physics book series (LNP, volume 273)

Abstract

This lecture is divided in four main sections. In the first one we study the general properties of harmonic polynomials, we derive various hyperspherical harmonic basis and we explain how to construct antisymmetric harmonic polynomials.

In the second part we introduce the Potential Harmonics for systems of bosons and for fermions, and we derive the coupled equations enabling one to describe the two-body correlations. In the third section it is shown that the infinite system of coupled differential equations of the Potential Harmonic expansion method can be reduce to a single integro-differential equation in two variables.

In the last section we present the Adiabatic Approximation in which the radial and orbital motions are decoupled and which provides a method for solving scattering states.

Keywords

Weight Function Quantum Number Couple Equation Adiabatic Approximation Schr6dinger Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • M. Fabre de la Ripelle
    • 1
  1. 1.Division de Physique ThéoriqueInstitut de Physique NucléaireOrsay CedexFrance

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