Hyperspherical Harmonics Expansion Techniques: Application to Problems in Physics
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.
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2 Systems of One or More Particles
3 ThreeBody System
4 General ManyBody Systems
5 The Trinucleon System
6 Application to Coulomb Systems
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Hyperspherical Harmonics Expansion Techniques: Application to Problems in ...
Tapan Kumar Das
No preview available - 2019
A-body adiabatic antisymmetric binding energy Bose–Einstein condensate bosons calculated Chakrabarti Chap coefficients convergence corresponding Coulomb systems coupled differential equation dilute discussed eigenvalue Fabre Faddeev component fermions Few-Body Syst few-body systems given by Eq GP equation Harmonics Expansion Techniques Hence HH basis HHEM hyperangles hyperangular hyperradius Hyperspherical Harmonics Expansion identical particles integral isospin isospin-spin Jacobi polynomials Jacobi vectors Kmax large number many-body Mathematical mixed symmetry neutron nuclear nuclei nucleon number of particles obtained optimal subset pair exchange PHEM Phys Physics potential harmonics potential matrix element potential multipole Quantum Mechanics quantum numbers relative motion repulsive Ripelle Schrödinger equation Sect Seiringer Sofianos solution solved space wave function spherical spherical harmonics spin wave symmetry components tensor three-body system total wave function totally antisymmetric totally symmetric two-body correlations two-body potential values wave function zero