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Hyperspherical harmonics expansion techniques[electronic resource] :application to problems in physics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.785
書名/作者:	Hyperspherical harmonics expansion techniques : application to problems in physics // by Tapan Kumar Das.
作者:	Das, Tapan Kumar.
出版者:	New Delhi : : Springer India :, 2016.
面頁冊數:	xi, 159 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Spherical harmonics.
標題:	Schrodinger equation.
標題:	Quantum theory.
標題:	Physics.
標題:	Numerical and Computational Physics.
標題:	Nuclear Physics, Heavy Ions, Hadrons.
標題:	Mathematical Methods in Physics.
標題:	Mathematical Physics.
ISBN:	9788132223610
ISBN:	9788132223603
內容註:	Introduction -- Systems of One or More Particles -- Three-body System -- General Many-body Systems -- The Trinucleon System -- Application to Coulomb Systems -- Potential Harmonics -- Application to Bose-Einstein Condensates -- Integro-differential Equation -- Computational Techniques.
摘要、提要註:	The book provides a generalized theoretical technique for solving the fewbody Schrodinger 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.
電子資源:	http://dx.doi.org/10.1007/978-81-322-2361-0

Hyperspherical harmonics expansion techniques[electronic resource] :application to problems in physics /
Das, Tapan Kumar.

Hyperspherical harmonics expansion techniquesapplication to problems in physics /[electronic resource] :by Tapan Kumar Das. - New Delhi :Springer India :2016. - xi, 159 p. :ill., digital ;24 cm. - Theoretical and mathematical physics,1864-5879. - Theoretical and mathematical physics..

Introduction -- Systems of One or More Particles -- Three-body System -- General Many-body Systems -- The Trinucleon System -- Application to Coulomb Systems -- Potential Harmonics -- Application to Bose-Einstein Condensates -- Integro-differential Equation -- Computational Techniques.

The book provides a generalized theoretical technique for solving the fewbody Schrodinger 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.

ISBN: 9788132223610

Standard No.: 10.1007/978-81-322-2361-0doiSubjects--Topical Terms:

468444
Spherical harmonics.

LC Class. No.: QC20.7.S645

Dewey Class. No.: 515.785

Hyperspherical harmonics expansion techniques[electronic resource] :application to problems in physics /
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520 $a The book provides a generalized theoretical technique for solving the fewbody Schrodinger 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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