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## Rotating Black Holes

*Valeri P. Frolov and Andrei Zelnikov*

### in Introduction to Black Hole Physics

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199692293
- eISBN:
- 9780191731860
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199692293.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

The Chapter is devoted to rotating black holes, their properties, global structure, and study particle and light motion in their gravitational field. We introduce and explain notions of the horizon ... More

## Hamilton–Jacobi theory

*S. G. Rajeev*

### in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0009
- Subject:
- Physics, Atomic, Laser, and Optical Physics

This chapter derives the Hamilton-Jacobi equation. Euler's two centre problem is solved by using separation of variables in the elliptical co-ordinate system. The connection to the eikonal equation ... 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

## 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

## Analytic Element Method: Complex Interactions of Boundaries and Interfaces

*David R. Steward*

- Published in print:
- 2020
- Published Online:
- November 2020
- ISBN:
- 9780198856788
- eISBN:
- 9780191890031
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198856788.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the ... More

## A First Example: The “Particle in a Box“ and Quantized Translational Motion

*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/9780190920807.003.0005
- Subject:
- Chemistry, Quantum and Theoretical Chemistry

The simple ‘particle in a box’ (Piab) is introduced in this chapter so that the reader can get familiar with applying the quantum recipe and atomic units. The PiaB is introduced in its one, two, and ... 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

## Wave Mechanics & Elements of Mathematical Physics

*Peter Mann*

### in Lagrangian and Hamiltonian Dynamics

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents an in-depth look at classical wave mechanics and mathematical physics, containing key examples directly relevant to molecular physics. The separation of variables is used to ... More

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