Hyperspherical Harmonics Expansion Techniques

Application to Problems in Physics

Nonfiction, Science & Nature, Science, Physics, Nuclear Physics, Mathematical Physics
Cover of the book Hyperspherical Harmonics Expansion Techniques by Tapan Kumar Das, Springer India
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Tapan Kumar Das ISBN: 9788132223610
Publisher: Springer India Publication: November 26, 2015
Imprint: Springer Language: English
Author: Tapan Kumar Das
ISBN: 9788132223610
Publisher: Springer India
Publication: November 26, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer India

Cover of the book GHG Emissions and Economic Growth by Tapan Kumar Das
Cover of the book Channel Coding Techniques for Wireless Communications by Tapan Kumar Das
Cover of the book Free Space Optical Communication by Tapan Kumar Das
Cover of the book High Dimensional Neurocomputing by Tapan Kumar Das
Cover of the book Early Software Reliability Prediction by Tapan Kumar Das
Cover of the book Potassium Solubilizing Microorganisms for Sustainable Agriculture by Tapan Kumar Das
Cover of the book Market, Regulations and Finance by Tapan Kumar Das
Cover of the book Probiotics and Bioactive Carbohydrates in Colon Cancer Management by Tapan Kumar Das
Cover of the book Chitin and Chitosan for Regenerative Medicine by Tapan Kumar Das
Cover of the book Fundamentals of Physical Geology by Tapan Kumar Das
Cover of the book Financial Access of the Urban Poor in India by Tapan Kumar Das
Cover of the book Proceedings of International Conference on Advances in Tribology and Engineering Systems by Tapan Kumar Das
Cover of the book Intelligent Computing, Communication and Devices by Tapan Kumar Das
Cover of the book Nature, Economy and Society by Tapan Kumar Das
Cover of the book Proceedings of International Conference on Soft Computing Techniques and Engineering Application by Tapan Kumar Das
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy