Variational methods for the few-body bound state in a harmonic oscillator basis

  • Sidney A. Coon
  • Oyanarte Portilho
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)


The method of expanding the trial variational function into a complete set of harmonic oscillator functions is reviewed. The formalism for the two body and three-body bound state is given. The treatment of two equal-mass bosons and a third boson of different mass is elaborated. Model calculations of quarkonium are compared with exact results and with integral equation methods. The convergence of a model 3u system is studied in detail, and the role of Jastrow-type correlations is examined. Phenomenological studies reviewed include realistic models of quarkonium, alpha-particle models of this carbon nucleus, and alpha-particle models of singly and doubly strange hypernuclei. The latter studies employed the best available phenomenological αα interactions.


Harmonic Oscillator Trial Function Hamiltonian Matrix Trial Wave Function Variational Wave Function 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Sidney A. Coon
    • 1
  • Oyanarte Portilho
    • 2
  1. 1.Department of PhysicsUniversity of ArizonaTucsonUSA
  2. 2.Departamento de FisicaUniversidade de BrasiliaBrasilia-DFBrazil

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