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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


Introduction to Quantum Theory

Wai-Kee Li, Gong-Du Zhou, and Thomas Chung Wai Mak

in Advanced Structural Inorganic Chemistry

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199216949
eISBN:
9780191711992
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199216949.003.0001
Subject:
Physics, Crystallography: Physics

This chapter covers the rudiments of quantum theory, including the dual nature of light and matter, the Uncertainty Principle and probability concept, the electronic wavefunction, and the probability ... More


ELECTRONIC STRUCTURE OF THE PERFECT LATTICE

A.M. Stoneham

in Theory of Defects in Solids: Electronic Structure of Defects in Insulators and Semiconductors

Published in print:
2001
Published Online:
September 2007
ISBN:
9780198507802
eISBN:
9780191709920
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507802.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines the major assumptions and approximations in electronic structure calculations for perfect solids. It emphasizes those issues that are important in defect studies, such as the ... More


Quantum chemistry

ANGELO GAVEZZOTTI

in Molecular Aggregation: Structure analysis and molecular simulation of crystals and liquids

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198570806
eISBN:
9780191718779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570806.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

In the early decades of the 20th century, a large and convincing body of experimental evidence pointed to the fact that atomic particles share some properties of massive bodies and some properties of ... More


Visualizing Critical Correlations Near the Metal–Insulator Transition in Ga1−x Mn x As

Ali Yazdani

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Electronic states in disordered conductors on the verge of localization are predicted to exhibit critical spatial characteristics indicative of the proximity to a metal- insulator phase transition. ... More


Introduction to Scanning Tunneling Microscopy

C. Julian Chen

Published in print:
2021
Published Online:
April 2021
ISBN:
9780198856559
eISBN:
9780191889905
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198856559.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

The scanning tunnelling microscope (STM) was invented by Binnig and Rohrer and received a Nobel Prize of Physics in 1986. Together with the atomic force microscope (AFM), it enables non-destructive ... 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


What is a Quantum Superposition?

Gershon Kurizki and Goren Gordon

in The Quantum Matrix: Henry Bar's Perilous Struggle for Quantum Coherence

Published in print:
2020
Published Online:
July 2020
ISBN:
9780198787464
eISBN:
9780191829512
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198787464.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

Henry has successfully tested the Split button of his quantum suit that enables a quantum object to be in several places at the same time. This bizarre phenomenon is explained by the superposition ... More


Anderson localization of ultracold atoms in a laser speckle

Alain Aspect

in Many-Body Physics with Ultracold Gases: Lecture Notes of the Les Houches Summer School: Volume 94, July 2010

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199661886
eISBN:
9780191748356
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199661886.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter shows that ultracold atoms placed in an optical disordered potential form an excellent system to study Anderson localization (AL) experimentally. The discussion covers AL for the ... More


Approximations to Exact Perturbation and Response Theory Expressions

Stephan P. A. Sauer

in Molecular Electromagnetism: A Computational Chemistry Approach

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199575398
eISBN:
9780191775109
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575398.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter derives computational chemistry methods for calculating molecular properties. It approximates the exact unperturbed wavefunctions and the complete set of operators in the expression for ... More


Identical particles; Second quantization

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter analyzes issues that deal with quantum statistics (symmetry of wavefunctions); elements of the second quantization formalism (the occupation-number representation); and the simplest ... More


Quasi-classical approximation; 1/N-expansion in quantum mechanics

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0009
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter deals with problems related to quasi-classical energy quantization; quasi-classical wavefunctions, probabilities, and mean values; penetration through potential barriers; and ... More


Radiative transitions

B. K. Ridley FRS

in Quantum Processes in Semiconductors

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199677214
eISBN:
9780191760624
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199677214.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

An electromagnetic field with a Lorentz-gauge vector potential and a scalar potential equal to zero can induce disturbance in an electron. In general, this disturbance can be considered a small ... More


Excitons in conjugated polymers

William Barford

in Electronic and Optical Properties of Conjugated Polymers

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199677467
eISBN:
9780191757402
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199677467.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

Excitons are the primary photo-excited states in conjugated polymers. This chapter develops effective-particle models of excitons in the weak and strong-coupling limits. Excitons are classified as ... More


Computer-Aided Chemistry

Mark Ladd

in Bonding, Structure and Solid-State Chemistry

Published in print:
2016
Published Online:
May 2016
ISBN:
9780198729945
eISBN:
9780191818783
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198729945.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the various programs that have been devised to accompany the text, using both Python and Fortran programs, some of which are interactive. The topics that are programmed and ... More


Imaging Wavefunctions

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/9780198856559.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

The concept of wavefunction was introduced in the first 1926 paper by Erwin Schrödinger as the central object of the atomic world and the cornerstone of quantum mechanics. It is a mathematical ... More


Dirac’s Derivation of the Relativistic Wave Equation: Electron Spin and Antimatter

Jim Baggott

in The Quantum Cookbook: Mathematical Recipes for the Foundations for Quantum Mechanics

Published in print:
2020
Published Online:
January 2020
ISBN:
9780198827856
eISBN:
9780191866579
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827856.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The problem of electron spin was in some way connected with special relativity. Dirac’s fascination with relativity and his already burgeoning reputation made the search for a fully relativistic form ... More


Heisenberg’s Derivation of the Pauli Exclusion Principle: The Stability of Matter and the Periodic Table

Jim Baggott

in The Quantum Cookbook: Mathematical Recipes for the Foundations for Quantum Mechanics

Published in print:
2020
Published Online:
January 2020
ISBN:
9780198827856
eISBN:
9780191866579
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827856.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Despite the success of Schrödinger’s description of the H-atom, it became apparent that the spectrum of the simplest multi-electron atom—helium—could not be so readily explained. And the spectra of ... More


Superfluidity and Superconductivity

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/9780198791942.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The ... More


The Periodic Table Retrieved from Density Functional Theory Based Concepts: The Electron Density, the Shape Function and the Linear Response Function

Paul Geerlings

in Mendeleev to Oganesson: A Multidisciplinary Perspective on the Periodic Table

Published in print:
2018
Published Online:
November 2020
ISBN:
9780190668532
eISBN:
9780197559765
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190668532.003.0011
Subject:
Chemistry, Physical Chemistry

“The periodic table of the elements is one of the most powerful icons in science: a single document that captures the essence of chemistry in an elegant pattern.” This statement taken from Eric ... More


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