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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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