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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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