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## Basic Theory and Techniques of the OLCAO Method

*Wai-yim Ching and Paul Rulis*

### in Electronic Structure Methods for Complex Materials: The orthogonalized linear combination of atomic orbitals

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199575800
- eISBN:
- 9780191740992
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199575800.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter provides the basic theory of the OLCAO method which is derived from the traditional LCAO method. Atomic orbitals are used in the basis expansion where the radial part is expanded in ... 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

## Bose Gas in One Dimension: Lieb–Liniger Model

*Hans-Peter Eckle*

### in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0015
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The coordinate Bethe ansatz can be extended to a model, the Lieb–Liniger model, of a one-dimensional gas of Bosons interacting with repulsive δ-function potentials. It has attracted attention due to ... More

## Bound states in one dimension

*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/9780198749349.003.0008
- Subject:
- Physics, Atomic, Laser, and Optical Physics

In this and in the following chapter, it reviews an important part of undergraduate material, namely solving for bound states and for scattering in one-dimension for the case where the potential is ... More

## A Hundred and One Years of Mechanics: Newton to Lagrange via Daniel Bernoulli

*Jennifer Coopersmith*

### in Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198716747
- eISBN:
- 9780191800955
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198716747.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Vis viva (kinetic energy) was discovered by Leibniz, and ‘s Gravesande’s experiments showed that both momentum and kinetic energy were important measures. The concept of ‘potential energy’ slowly ... More

## Hamilton and Green

*Jennifer Coopersmith*

### in Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198716747
- eISBN:
- 9780191800955
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198716747.003.0013
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

The unknown George Green, from Nottingham, self-published An Essay on the Mathematical Analysis of Electricity and Magnetism, in which the potential function, V, was defined for the first time. The ... More

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