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This book is a compilation of different methods of formulating and
solving inverse problems in physics from classical mechanics to the
potentials and nucleus-nucleus scattering. Mathematical proofs are
omitted since excellent monographs already exist dealing with these
aspects of the inverse problems.The emphasis here is on finding
numerical solutions to complicated equations. A detailed discussion
is presented on the use of continued fractional expansion, its
power and its limitation as applied to various physical problems.
In particular, the inverse problem for discrete form of the wave
equation is given a detailed exposition and applied to atomic and
nuclear scattering, in the latter for elastic as well as inelastic
collision. This technique is also used for inverse problem of
geomagnetic induction and one-dimensional electrical conductivity.
Among other topics covered are the inverse problem of torsional
vibration, and also a chapter on the determination of the motion of
a body with reflecting surface from its reflection coefficient.
Dissipative forces play an important role in problems of classical
as well as quantum mechanics. Since these forces are not among the
basic forces of nature, it is essential to consider whether they
should be treated as phenomenological interactions used in the
equations of motion, or they should be derived from other
conservative forces. In this book we discuss both approaches in
detail starting with the Stoke's law of motion in a viscous fluid
and ending with a rather detailed review of the recent attempts to
understand the nature of the drag forces originating from the
motion of a plane or a sphere in vacuum caused by the variations in
the zero-point energy. In the classical formulation, mathematical
techniques for construction of Lagrangian and Hamiltonian for the
variational formulation of non-conservative systems are discussed
at length. Various physical systems of interest including the
problem of radiating electron, theory of natural line width,
spin-boson problem, scattering and trapping of heavy ions and
optical potential models of nuclear reactions are considered and
solved.
Dissipative forces play an important role in problems of classical
as well as quantum mechanics. Since these forces are not among the
basic forces of nature, it is essential to consider whether they
should be treated as phenomenological interactions used in the
equations of motion, or they should be derived from other
conservative forces. In this book we discuss both approaches in
detail starting with the Stoke's law of motion in a viscous fluid
and ending with a rather detailed review of the recent attempts to
understand the nature of the drag forces originating from the
motion of a plane or a sphere in vacuum caused by the variations in
the zero-point energy. In the classical formulation, mathematical
techniques for construction of Lagrangian and Hamiltonian for the
variational formulation of non-conservative systems are discussed
at length. Various physical systems of interest including the
problem of radiating electron, theory of natural line width,
spin-boson problem, scattering and trapping of heavy ions and
optical potential models of nuclear reactions are considered and
solved.
In this revised and expanded edition, in addition to a
comprehensible introduction to the theoretical foundations of
quantum tunneling based on different methods of formulating and
solving tunneling problems, different semiclassical approximations
for multidimensional systems are presented. Particular attention is
given to the tunneling of composite systems, with examples taken
from molecular tunneling and also from nuclear reactions. The
interesting and puzzling features of tunneling times are given
extensive coverage, and the possibility of measurement of these
times with quantum clocks are critically examined.In addition, by
considering the analogy between evanescent waves in waveguides and
in quantum tunneling, the times related to electromagnetic wave
propagation have been used to explain certain aspects of quantum
tunneling times. These topics are treated in both non-relativistic
as well as relativistic regimes. Finally, a large number of
examples of tunneling in atomic, molecular, condensed matter and
nuclear physics are presented and solved.
This book provides a detailed account of quantum theory with a much
greater emphasis on the Heisenberg equations of motion and the
matrix method. No other texts have come close to discuss quantum
theory in terms of depth of coverage. The book features a deeper
treatment of the fundamental concepts such as the rules of
constructing quantum mechanical operators and the classical-quantal
correspondence; the exact and approximate methods based on the
Heisenberg equations; the determinantal approach to the scattering
theory and the LSZ reduction formalism where the latter method is
used to obtain the transition matrix. The uncertainty relations for
a number of different observables are derived and discussed. A
comprehensive chapter on the quantization of systems with
nonlocalized interaction is included. Exact solvable models, and
approximate techniques for solution of realistic many-body problems
are also considered. The book takes a unified look in the final
chapter, examining the question of measurement in quantum theory,
with an introduction to the Bell's inequalities.
This book provides a detailed account of quantum theory with a much
greater emphasis on the Heisenberg equations of motion and the
matrix method. No other texts have come close to discuss quantum
theory in terms of depth of coverage. The book features a deeper
treatment of the fundamental concepts such as the rules of
constructing quantum mechanical operators and the classical-quantal
correspondence; the exact and approximate methods based on the
Heisenberg equations; the determinantal approach to the scattering
theory and the LSZ reduction formalism where the latter method is
used to obtain the transition matrix. The uncertainty relations for
a number of different observables are derived and discussed. A
comprehensive chapter on the quantization of systems with
nonlocalized interaction is included. Exact solvable models, and
approximate techniques for solution of realistic many-body problems
are also considered. The book takes a unified look in the final
chapter, examining the question of measurement in quantum theory,
with an introduction to the Bell's inequalities.
With the fast pace of developments in quantum technologies, it is
more than ever necessary to make the new generation of students in
science and engineering familiar with the key ideas behind such
disruptive systems. This book intends to fill such a gap between
experts and non-experts in the field by providing the reader with
the basic tools needed to understand the latest developments in
quantum communications and its future directions. This is not only
to expand the audience knowledge but also to attract new talents to
this flourishing field. To that end, the book as a whole does not
delve into much detail and most often suffices to provide some
insight into the problem in hand. The primary users of the book
will then be students in science and engineering in their final
year of undergraduate studies or early years of their post-graduate
programmes.
With the fast pace of developments in quantum technologies, it is
more than ever necessary to make the new generation of students in
science and engineering familiar with the key ideas behind such
disruptive systems. This book intends to fill such a gap between
experts and non-experts in the field by providing the reader with
the basic tools needed to understand the latest developments in
quantum communications and its future directions. This is not only
to expand the audience knowledge but also to attract new talents to
this flourishing field. To that end, the book as a whole does not
delve into much detail and most often suffices to provide some
insight into the problem in hand. The primary users of the book
will then be students in science and engineering in their final
year of undergraduate studies or early years of their post-graduate
programmes.
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