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Theory of resonances. Principles and applications. (English) Zbl 0707.47009

Reidel Texts in the Mathematical Sciences, 3. Dordrecht etc.: Kluwer Academic Publishers. 355 p. Dfl. 180.00; $ 94.00; £57.00 (1989).
This book is a manual on the theory of resonance states and processes in nonrelativistic quantum mechanics on N-body systems. It fills the gap between the textbooks on the theory of resonance processes in quantum mechanics and the modern journal publications.
Chapter 1, in a very condensed form, acquaints the reader with subsidiary knowledge from various areas of mathematics, such as the theory of functions of complex variables, integral equations, estimation of divergent integrals, concise theory for the Padé approximants. This Chapter also gives necessary information about the Faddeev equations and the scattering theory.
Chapter 2 carefully discussed general information about resonance phenomena. It considers, in particular, Kapur-Peierls formalism, Gamow and Siegert states, R-matrix approach, etc. Chapter 3 contains discussion of the theory of resonance states for two and three particle systems on the basis of the Hilbert-Schmidt method from the theory of integral equations.
Chapter 4 describes projection formalism (due to H. Feshbach) of the studying of resonance phenomena arising in scattering and reaction. Chapter 5 deals with a new approach to the theory of resonance states and processes proposed by the authors. This approach is based on the analytic continuation of the S-matrix singularities in the coupling constant. Chapter 6 discusses a method proposed by the authors for determination of the resonance parameters (width, energies, etc.) from analysis of experimental data. In Chapter 7 several examples illustrating the methods from the previous chapters are presented. These examples dealt mostly with resonance processes in nuclear physics. the book is completed by the list of the open problems.
Reviewer: M.Perelmuter

MSC:

47A40 Scattering theory of linear operators
81U10 \(n\)-body potential quantum scattering theory
47N50 Applications of operator theory in the physical sciences
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
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