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Formal means

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0026
Subject:
Physics, Nuclear and Plasma Physics

This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, ... More


Time-harmonic fields

Mauro Fabrizio and Morro Angelo

in Electromagnetism of Continuous Media: Mathematical Modelling and Applications

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198527008
eISBN:
9780191713316
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527008.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter reviews balance laws and relevant solutions to Maxwell’s equations in connection with the time-harmonic dependence. The wave equation becomes the Helmholtz equation and, for it, Green’s ... More


Spherical-wave dynamical theory: I. Kato’s theory

ANDRÉ AUTHIER

in Dynamical Theory of X-Ray Diffraction

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198528920
eISBN:
9780191713125
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528920.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter is the first of two dealing with the dynamical diffraction of incident spherical waves. It makes use of Kato's theory, which is based on a Fourier expansion of the spherical wave. The ... More


Stationary phase and microlocal analysis

Christopher D. Sogge

in Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160757
eISBN:
9781400850549
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160757.003.0004
Subject:
Mathematics, Numerical Analysis

This chapter discusses basic techniques from the theory of stationary phase. After giving an overview of the method of stationary phase, the chapter moves on to a discussion of pseudodifferential ... More


Phase integral approximations

M. S. Child

in Semiclassical Mechanics with Molecular Applications

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199672981
eISBN:
9780191783227
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199672981.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

Phase integral approximations express the quantum wavefunction in terms of the classical action integral, S(x)=∫p(x)dx.The main aim of the chapter is to highlight the strengths and weaknesses of the ... More


Matrix elements

M. S. Child

in Semiclassical Mechanics with Molecular Applications

Published in print:
2014
Published Online:
October 2014
ISBN:
9780199672981
eISBN:
9780191783227
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199672981.003.0005
Subject:
Physics, Atomic, Laser, and Optical Physics

Two types of matrix element approximation are adopted according to whether the wavefunctions are taken in angle–action or normalized JWKB forms. The former gives the Heisenberg correspondence between ... More


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