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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


Analytic Elements from Separation of Variables

David R. Steward

in Analytic Element Method: Complex Interactions of Boundaries and Interfaces

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198856788
eISBN:
9780191890031
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198856788.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Separation of variables provides influence functions for analytic elements, which extend the solutions available with complex functions to problems involving the Helmholtz and modified Helmholtz ... 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


Particle in a Cylinder, in a Sphere, and on a Helix

Jochen Autschbach

in Quantum Theory for Chemical Applications: From Basic Concepts to Advanced Topics

Published in print:
2020
Published Online:
February 2021
ISBN:
9780190920807
eISBN:
9780197508350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190920807.003.0018
Subject:
Chemistry, Quantum and Theoretical Chemistry

The particle in a box from an earlier chapter is useful as a model to treat the electron motion in linear molecular ‘wires’, rectangular surfaces, and cuboid nano-particles. In this chapter, similar ... 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


Basic Statistical Mechanics

C. G. Gray and K. E. Gubbins

in Theory of Molecular Fluids: I: Fundamentals

Published in print:
1984
Published Online:
November 2020
ISBN:
9780198556022
eISBN:
9780191919251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198556022.003.0009
Subject:
Chemistry, Theoretical Chemistry

In this chapter we introduce distribution functions for molecular momenta and positions. All equilibrium properties of the system can be calculated if both the intermolecular potential energy and ... More


Guided Waves in Plates and Rods

Dale Chimenti, Stanislav Rokhlin, and Peter Nagy

in Physical Ultrasonics of Composites

Published in print:
2011
Published Online:
November 2020
ISBN:
9780195079609
eISBN:
9780197560389
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195079609.003.0009
Subject:
Chemistry, Industrial Chemistry

In this chapter we consider elastic wave modes which propagate in composites with finite boundaries. There are those waves that exist between the two plane parallel boundaries of a homogeneous ... More


Tunneling Matrix Elements

C. Julian Chen

in Introduction to Scanning Tunneling Microscopy

Published in print:
2021
Published Online:
April 2021
ISBN:
9780198856559
eISBN:
9780191889905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198856559.003.0003
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


Measurement of Scattering Coefficients

Dale Chimenti, Stanislav Rokhlin, and Peter Nagy

in Physical Ultrasonics of Composites

Published in print:
2011
Published Online:
November 2020
ISBN:
9780195079609
eISBN:
9780197560389
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195079609.003.0012
Subject:
Chemistry, Industrial Chemistry

In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that ... More


Diffusion and Drug Dispersion

W. Mark Saltzman

in Drug Delivery: Engineering Principles for Drug Therapy

Published in print:
2001
Published Online:
November 2020
ISBN:
9780195085891
eISBN:
9780197560501
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195085891.003.0008
Subject:
Chemistry, Medicinal Chemistry

Most biological processes occur in an environment that is predominantly water: a typical cell contains 70-85% water and the extracellular space of most tissues is 99%. Even the brain, with its ... More


Controlled Drug Delivery Systems

W. Mark Saltzman

in Drug Delivery: Engineering Principles for Drug Therapy

Published in print:
2001
Published Online:
November 2020
ISBN:
9780195085891
eISBN:
9780197560501
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195085891.003.0015
Subject:
Chemistry, Medicinal Chemistry

In most forms of drug delivery, spatial localization and duration of drug concentration are constrained by organ physiology and metabolism. For example, drugs administered orally will distribute to ... 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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