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## Classical Scattering Theory

*Peter Monk*

### in Finite Element Methods for Maxwell's Equations

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198508885
- eISBN:
- 9780191708633
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508885.003.0009
- Subject:
- Mathematics, Numerical Analysis

This chapter presents basic tools for studying the scattering problem. The Stratton-Chu integral representation of the electromagnetic field is derived as well as the far field pattern of the ... More

## Tunneling Matrix Elements

*C. Julian Chen*

### in Introduction to Scanning Tunneling Microscopy: Second Edition

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199211500
- eISBN:
- 9780191705991
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211500.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter presents systematic methods to evaluate the tunneling matrix elements in the Bardeen tunneling theory. A key problem in applying the Bardeen tunneling theory to STM is the evaluation of ... More

## Bound states in spherically symmetric potentials

*Efstratios Manousakis*

### in Practical Quantum Mechanics: Modern Tools and Applications

- Published in print:
- 2015
- Published Online:
- December 2015
- ISBN:
- 9780198749349
- eISBN:
- 9780191813474
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198749349.003.0016
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter deals with bound states in the case where the potential is spherically symmetric. As a result, it discusses the spherical Bessel equation, the spherical Bessel and Newmann functions and ... More

## Special functions

*Chun Wa Wong*

### in Introduction to Mathematical Physics: Methods & Concepts

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199641390
- eISBN:
- 9780191747786
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641390.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Special functions are advanced functions frequently used in science and engineering. The properties of Legendre, Hermite, Laguerre, Chebyshev and spherical harmonics polynomials and Bessel functions ... More

## Mathematical Appendices

*Abraham Bers*

### in Plasma Physics and Fusion Plasma Electrodynamics

- Published in print:
- 2016
- Published Online:
- November 2016
- ISBN:
- 9780199295784
- eISBN:
- 9780191749063
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199295784.003.0033
- Subject:
- Physics, Nuclear and Plasma Physics, Particle Physics / Astrophysics / Cosmology

This concluding chapter addresses accounting for the remaining single-charged particle fields in a plasma, which are neglected in a fluid kinetic description: those associated with radiations and ... More

## Pulsatile Flows

*Troy Shinbrot*

### in Biomedical Fluid Dynamics: Flow and Form

- Published in print:
- 2019
- Published Online:
- June 2019
- ISBN:
- 9780198812586
- eISBN:
- 9780191850721
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198812586.003.0004
- Subject:
- Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Flow solutions in the presence of pulsation (e.g. from the heart) are developed. Bessel functions are introduced as an aside. The concepts of shocks and solitary waves (solitons) are then discussed ... More

## Introduction to the WKB(J) Approximation: All Things Airy

*John A. Adam*

### in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691148373
- eISBN:
- 9781400885404
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148373.003.0007
- Subject:
- Mathematics, Applied Mathematics

This chapter deals with the WKB(J) approximation, commonly used in applied mathematics and mathematical physics to find approximate solutions of linear ordinary differential equations (of any order ... More

## Diffraction of Light from Blood Cells

*Robert N. Compton and Michael A. Duncan*

### in Laser Experiments for Chemistry and Physics

- Published in print:
- 2015
- Published Online:
- December 2015
- ISBN:
- 9780198742975
- eISBN:
- 9780191816932
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198742975.003.0030
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The picture on the front of this book shows the diffraction pattern from a laser beam passing through a pinhole. The experiment in this chapter uses Babinet’s principle to analyze the diffraction of ... More

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