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## Mathematics and Physics: Strategies of Assimilation

*Alasdair Urquhart*

### in The Philosophy of Mathematical Practice

- Published in print:
- 2008
- Published Online:
- February 2010
- ISBN:
- 9780199296453
- eISBN:
- 9780191711961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296453.003.0017
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

The main topic of this chapter is the problem posed to the mathematical community by the non-rigorous methods used by physicists in investigating mathematical problems. These methods are often highly ... More

## Continuous Random Numbers

*Robert H. Swendsen*

### in An Introduction to Statistical Mechanics and Thermodynamics

- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199646944
- eISBN:
- 9780191775123
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199646944.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter extends the development of probability theory to include continuous random variables. Dirac delta functions are used to simplify the transformation of continuous random variables, as ... More

## Fourier series and Fourier transforms

*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/9780199641390.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The Fourier expansion of an arbitrary piecewise-smooth function in the finite interval —π 〈 x 〈 π as an infinite sum of terms (a 0; a n ... More

## Retarded Green’s Functions

*Norman J. Morgenstern Horing*

### in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198791942
- eISBN:
- 9780191834165
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791942.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, ... More

## Molecular Scattering and Fourier Transforms

*Peter B. Moore*

### in Visualizing the Invisible: Imaging Techniques for the Structural Biologist

- Published in print:
- 2012
- Published Online:
- May 2015
- ISBN:
- 9780199767090
- eISBN:
- 9780190267841
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:osobl/9780199767090.003.0002
- Subject:
- Biology, Biochemistry / Molecular Biology

This chapter explores the mathematical relationships existing between known molecular structures from Chapter 1 and the structure factors, particularly dealing with the Fourier transforms and Fourier ... More

## Free Particle, Wave Packet and Dynamics, Quantum Dots, Defects and Traps

*Duncan G. Steel*

### in Introduction to Quantum Nanotechnology: A Problem Focused Approach

- Published in print:
- 2021
- Published Online:
- July 2021
- ISBN:
- 9780192895073
- eISBN:
- 9780191924149
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192895073.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter continues with a study of the time independent Schrödinger equation and seeks to contrast the quantum behavior of a free particle with that of a particle localized in a potential quantum ... More

## Nano-Mechanical Oscillator and Basic Dynamics: Part I

*Duncan G. Steel*

### in Introduction to Quantum Nanotechnology: A Problem Focused Approach

- Published in print:
- 2021
- Published Online:
- July 2021
- ISBN:
- 9780192895073
- eISBN:
- 9780191924149
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780192895073.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This discussion introduces the student to the reality, in quantum technology, that analysis of any problem necessarily begins with the Hamiltonian representing the system. The quantum Hamiltonian ... More

## Soil Properties and Water Movement

*J. -Y. Parlange and T. S. Steenhuis*

### in Vadose Zone Hydrology: Cutting Across Disciplines

- Published in print:
- 1999
- Published Online:
- November 2020
- ISBN:
- 9780195109900
- eISBN:
- 9780197561058
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195109900.003.0008
- Subject:
- Earth Sciences and Geography, Oceanography and Hydrology

For all spatial scales, from pore through local and field, to a watershed, interaction of the land surface with the atmosphere will be one of the crucial topics in hydrology and environmental ... More

## Differential equations in physics

*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/9780199641390.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Ordinary and partial differential equations appear in physics as equations of motion or of state. They are often linear differential equations for which a sum of solutions remains a solution. The ... More

## Some essential mathematics

*J. Pierrus*

### in Solved Problems in Classical Electromagnetism: Analytical and Numerical Solutions with Comments

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198821915
- eISBN:
- 9780191861055
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821915.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter introduces most of the important mathematics that will be used repeatedly throughout this book. Whilst scalars like the electric potential Ф and the vector fields E and B are familiar ... 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

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