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Hyperspherical Harmonics Expansion Techniques - Application to Problems in Physics (Paperback, Softcover reprint of the original 1st ed. 2016)
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Hyperspherical Harmonics Expansion Techniques - Application to Problems in Physics (Paperback, Softcover reprint of the original 1st ed. 2016)
Series: Theoretical and Mathematical Physics
Expected to ship within 10 - 15 working days
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The book provides a generalized theoretical technique for solving
the fewbody Schroedinger 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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