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Linear Operators and Dyadics

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0007
Subject:
Physics, Atomic, Laser, and Optical Physics

Linear vector functions of vectors, and the related dyadic notation, are important in the study of rigid body motion and the covariant formulations of relativistic mechanics. These functions have a ... More


Operators

Gary E. Bowman

in Essential Quantum Mechanics

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228928
eISBN:
9780191711206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228928.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter develops a basic working knowledge of operators — objects central to quantum mechanics. The fact that quantum operators are linear determines how they may be manipulated, so linearity ... More


Mixture Models

R. Duncan Luce

in Response Times: Their Role in Inferring Elementary Mental Organization

Published in print:
1991
Published Online:
January 2008
ISBN:
9780195070019
eISBN:
9780199869879
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195070019.003.0007
Subject:
Psychology, Cognitive Models and Architectures

This chapter examines models that attempt to formulate amy information the mind has about the signals presented and how the mind then makes decisions about what and when to respond. Topics discussed ... More


Operators 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/9780199232710.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

Mathematical formalism of quantum mechanics is closely connected with the theory of linear operators. A key quantum-mechanical principle is that physical quantities (observables) are represented by ... More


Car Parking as a Game Between Simple Heuristics

John M. C. Hutchinson, Carola Fanselow, and Peter M. Todd

in Ecological Rationality: Intelligence in the World

Published in print:
2012
Published Online:
May 2012
ISBN:
9780195315448
eISBN:
9780199932429
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195315448.003.0133
Subject:
Psychology, Cognitive Psychology, Human-Technology Interaction

Selecting a parking space is a sequential-search problem, with the pattern of spaces available to search determined by where others have parked. Earlier optimality models of parking ignored this ... More


Linear Differential Polynomials

Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

in Asymptotic Differential Algebra and Model Theory of Transseries

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691175423
eISBN:
9781400885411
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175423.003.0006
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter introduces the reader to linear differential polynomials. It first considers homogeneous differential polynomials and the corresponding linear operators before proving various basic ... More


Kinematics of Rotation

Oliver Davis Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2011
Published Online:
December 2013
ISBN:
9780191001628
eISBN:
9780191775161
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780191001628.003.0008
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter discusses and develops the techniques needed to define the location and orientation of a moving rigid body. Roughly speaking, rotation can be defined as what a rigid body does. For ... More


Preliminaries to Main Results

Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav

in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.003.0009
Subject:
Mathematics, Analysis

This chapter presents a number of results and notions that will be used in subsequent chapters. In particular, it considers the concept of regular differentiability and the lemma on deformation of ... More


Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length

Camil Muscalu, Terence Tao, and Christoph Thiele

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0014
Subject:
Mathematics, Numerical Analysis

This chapter introduces two sets of theorems based on a study of the Littlewood–Paley boundedness properties of a tri-linear operator. It generalizes and proves similar estimates for multi-linear ... More


Linear Operators in Banach Spaces

D. E. Edmunds and W. D. Evans

in Spectral Theory and Differential Operators

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198812050
eISBN:
9780191861130
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812050.003.0001
Subject:
Mathematics, Pure Mathematics

Three main themes run through this chapter: compact linear operators, measures of non-compactness, and Fredholm and semi-Fredholm maps. Connections are established between these themes so as to ... More


Spectral Theory and Differential Operators

David Edmunds and Des Evans

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198812050
eISBN:
9780191861130
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812050.001.0001
Subject:
Mathematics, Pure Mathematics

This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and ... More


Identical Particles and Second Quantization: Occupation Number Representation

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/9780198791942.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized ... More


Linear Algebra and the Dirac Notation

Phillip Kaye, Raymond Laflamme, and Michele Mosca

in An Introduction to Quantum Computing

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198570004
eISBN:
9780191916724
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198570004.003.0005
Subject:
Computer Science, Computer Architecture and Logic Design

We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum ... More


Eventual Quantities, Immediate Extensions, and Special Cuts

Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

in Asymptotic Differential Algebra and Model Theory of Transseries

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691175423
eISBN:
9781400885411
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175423.003.0012
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter deals with eventual quantities, immediate extensions, and special cuts. It first considers the behavior of eventual quantities before discussing Newton weight, Newton degree, and Newton ... More


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