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Dirac's formalism of quantum mechanics was always praised for its
elegance. This book introduces the student to its mathematical
foundations and demonstrates its ease of applicability to problems
in quantum physics. The book starts by describing in detail the
concept of Gel'fand triplets and how one can make use of them to
make the Dirac heuristic approach rigorous. The results are then
deepened by giving the analytic tools, such as the Hardy class
function and Hilbert and Mellin transforms, needed in applications
to physical problems. Next, the RHS model for decaying states based
on the concept of Gamow vectors is presented. Applications are
given to physical theories of such phenomena as decaying states and
resonances.
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