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＜電子ブック＞
Wave Packet Analysis of Feynman Path Integrals / by Fabio Nicola, S. Ivan Trapasso
(Lecture Notes in Mathematics. ISSN:16179692 ; 2305)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XIII, 214 p. 3 illus. in color : online resource
著者標目	*Nicola, Fabio author Trapasso, S. Ivan author SpringerLink (Online service)
件　名	LCSH:Quantum physics LCSH:Functional analysis FREE:Quantum Physics FREE:Functional Analysis
一般注記	The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the wayto a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years HTTP:URL=https://doi.org/10.1007/978-3-031-06186-8

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