Hyperspherical Harmonics Expansion Techniques

Application to Problems in Physics

  • Tapan Kumar Das

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Tapan Kumar Das
    Pages 1-4
  3. Tapan Kumar Das
    Pages 5-16
  4. Tapan Kumar Das
    Pages 17-32
  5. Tapan Kumar Das
    Pages 33-54
  6. Tapan Kumar Das
    Pages 55-82
  7. Tapan Kumar Das
    Pages 83-94
  8. Tapan Kumar Das
    Pages 95-104
  9. Tapan Kumar Das
    Pages 105-124
  10. Tapan Kumar Das
    Pages 125-139
  11. Tapan Kumar Das
    Pages 141-156
  12. Back Matter
    Pages 157-159

About this book


The book provides a generalized theoretical technique for solving the fewbody Schrödinger equation. Straight forward approaches to solve it in terms of position vectors of constituent particles and using standard mathematical techniques become too cumbersome and inconvenient when the system contains more than two particles. The introduction of Jacobi vectors, hyperspherical variables and hyperspherical harmonics as an expansion basis is an elegant way to tackle systematically the problem of an increasing number of interacting particles. Analytic expressions for hyperspherical harmonics, appropriate symmetrisation of the wave function under exchange of identical particles and calculation of matrix elements of the interaction have been presented. Applications of this technique to various problems of physics have been discussed. In spite of straight forward generalization of the mathematical tools for increasing number of particles, the method becomes computationally difficult for more than a few particles. Hence various approximation methods have also been discussed. Chapters on the potential harmonics and its application to Bose-Einstein condensates (BEC) have been included to tackle dilute system of a large number of particles. A chapter on special numerical algorithms has also been provided. This monograph is a reference material for theoretical research in the few-body problems for research workers starting from advanced graduate level students to senior scientists.


Bose-Einstein Condensates Few-body Problems Hyperspherical Harmonics Trinucleon System Trinucleon Systems Two Electron Atoms

Authors and affiliations

  • Tapan Kumar Das
    • 1
  1. 1.Department of PhysicsUniversity of Calcutta, Department of PhysicsKolkataIndia

Bibliographic information