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Following Witten's remarkable discovery of the quantum mechanical
scheme in which all the salient features of supersymmetry are
embedded, SCQM (supersymmetric classical and quantum mechanics) has
become a separate area of research . In recent years, progress in
this field has been dramatic and the literature continues to grow.
Until now, no book has offered an overview of the subject with
enough detail to allow readers to become rapidly familiar with its
key ideas and methods. Supersymmetry in Classical and Quantum
Mechanics offers that overview and summarizes the major
developments of the last 15 years. It provides both an up-to-date
review of the literature and a detailed exposition of the
underlying SCQM principles. For those just beginning in the field,
the author presents step-by-step details of most of the
computations. For more experienced readers, the treatment includes
systematic analyses of more advanced topics, such as quasi- and
conditional solvability and the role of supersymmetry in nonlinear
systems.
Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods.
Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.
Partial Differential Equations for Mathematical Physicists is
intended for graduate students, researchers of theoretical physics
and applied mathematics, and professionals who want to take a
course in partial differential equations. This book offers the
essentials of the subject with the prerequisite being only an
elementary knowledge of introductory calculus, ordinary
differential equations, and certain aspects of classical mechanics.
We have stressed more the methodologies of partial differential
equations and how they can be implemented as tools for extracting
their solutions rather than dwelling on the foundational aspects.
After covering some basic material, the book proceeds to focus
mostly on the three main types of second order linear equations,
namely those belonging to the elliptic, hyperbolic, and parabolic
classes. For such equations a detailed treatment is given of the
derivation of Green's functions, and of the roles of
characteristics and techniques required in handling the solutions
with the expected amount of rigor. In this regard we have discussed
at length the method of separation variables, application of
Green's function technique, and employment of Fourier and Laplace's
transforms. Also collected in the appendices are some useful
results from the Dirac delta function, Fourier transform, and
Laplace transform meant to be used as supplementary materials to
the text. A good number of problems is worked out and an equally
large number of exercises has been appended at the end of each
chapter keeping in mind the needs of the students. It is expected
that this book will provide a systematic and unitary coverage of
the basics of partial differential equations. Key Features An
adequate and substantive exposition of the subject. Covers a wide
range of important topics. Maintains mathematical rigor throughout.
Organizes materials in a self-contained way with each chapter
ending with a summary. Contains a large number of worked out
problems.
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