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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.
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.
This book provides a clear understanding of quantum mechanics (QM)
by developing it from fundamental postulates in an axiomatic
manner, as its central theme. The target audience is physics
students at master’s level. It avoids historical developments,
which are piecemeal, not logically well knitted, and may lead to
misconceptions. Instead, in the present approach all of QM and all
its rules are developed logically starting from the fundamental
postulates only and no other assumptions. Specially noteworthy
topics have been developed in a smooth contiguous fashion following
the central theme. They provide a new approach to understanding QM.
In most other texts, these are presented as disjoint separate
topics. Since the reader may not be acquainted with advanced
mathematical topics like linear vector space, a number of such
topics have been presented as “mathematical preliminary.”
Standard topics, viz. derivation of uncertainty relations, simple
harmonic oscillator by operator method, bound systems in one and
three dimensions, angular momentum, hydrogen-like atom, and
scattering in one and three dimensions, are woven into the central
theme. Advanced topics like approximation methods, spin and
generalized angular momenta, addition of angular momenta, and
relativistic quantum mechanics have been reserved for Volume II.
The information of this book could be of use for the students,
researcher any person willing to know about the subject of
nutritional management of livestock, poultry and other animal
species. Information is presented in a simple, lucid manner and
concise form for the wide range of readers, academicians and
researchers.
Nach heutigem Stand der Forschung ist das dezimale Zahlensystem mit
dem Stellenwert und der Null zuerst in Indien belegt. Anhand der
indischen Quellen zeigt der Verfasser, dass es sich bei diesem
System nicht um eine einmalige Erfindung einer einzelnen Person
bzw. einer Schule handelte. Es entstand allmahlich in der Zeit
zwischen dem 5. Jh. und dem 6. Jh. durch einen Prozess des
Zusammenwirkens von drei unterschiedlichen Zahlensystemen. Das
Zeichen des Kreises fur die Null ist aus der graphischen
Darstellung der Ziffer 10 eines alteren Zahlensystems
hervorgegangen.
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