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Wave packet analysis of Feynman path integrals
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Wave packet analysis of Feynman path integralsby Fabio Nicola, S. Ivan Trapasso.
作者:
Nicola, Fabio.
其他作者:
Trapasso, S. Ivan.
出版者:
Cham :Springer International Publishing :2022.
面頁冊數:
xiii, 214 p. :ill., digital ;24 cm.
Contained By:
Springer Nature eBook
標題:
Quantum theory.
電子資源:
https://doi.org/10.1007/978-3-031-06186-8
ISBN:
9783031061868$q(electronic bk.)
Wave packet analysis of Feynman path integrals
Nicola, Fabio.
Wave packet analysis of Feynman path integrals
[electronic resource] /by Fabio Nicola, S. Ivan Trapasso. - Cham :Springer International Publishing :2022. - xiii, 214 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23051617-9692 ;. - Lecture notes in mathematics ;2035..
The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets - can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.
ISBN: 9783031061868$q(electronic bk.)
Standard No.: 10.1007/978-3-031-06186-8doiSubjects--Topical Terms:
199020
Quantum theory.
LC Class. No.: QC174.17.F45 / N53 2022
Dewey Class. No.: 530.12
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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 way to 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.
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