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The Quantum Mechanical State

David Hodgson

in The Mind Matters: Consciousness and Choice in a Quantum World

Published in print:
1993
Published Online:
October 2011
ISBN:
9780198240686
eISBN:
9780191680236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198240686.003.0012
Subject:
Philosophy, Philosophy of Mind, Metaphysics/Epistemology

In classical physics, the ‘state’ of a particle, at any particular time, is taken to involve a definite position in space and a definite motion; and the state of a system of particles is taken to ... More


Abstract Linear Space of State Vectors

P.J.E. Peebles

in Quantum Mechanics

Published in print:
2019
Published Online:
May 2021
ISBN:
9780691209821
eISBN:
9780691206738
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691209821.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses abstract linear space of state vectors. The wave mechanics presented in the previous chapter is easily generalized for use in all the applications of quantum mechanics ... More


Matrix Mechanics

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/9780199228928.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the matrix-mechanics formulation of quantum mechanics, emphasizing both calculational techniques and conceptual understanding. Parallels between matrix mechanics and ordinary ... More


Measurement Theory

P.J.E. Peebles

in Quantum Mechanics

Published in print:
2019
Published Online:
May 2021
ISBN:
9780691209821
eISBN:
9780691206738
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691209821.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter reviews measurement theory in quantum mechanics. The measurement prescription in quantum mechanics can be stated in a few lines and has found an enormous range of applications, in all of ... More


Combined Systems

David Hodgson

in The Mind Matters: Consciousness and Choice in a Quantum World

Published in print:
1993
Published Online:
October 2011
ISBN:
9780198240686
eISBN:
9780191680236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198240686.003.0014
Subject:
Philosophy, Philosophy of Mind, Metaphysics/Epistemology

This chapter discusses the application of quantum physics to one-dimensional motion of multiple particles and indicates how the principles apply to dealing at once with all aspects of one particle. ... More


Particle Learning for Sequential Bayesian Computation *

Hedibert F. Lopes, Michael S. Johannes, Carlos M. Carvalho, and Nicholas G. Polson

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0011
Subject:
Mathematics, Probability / Statistics

Particle learning provides a simulation‐based approach to sequential Bayesian computation. To sample from a posterior distribution of interest we use an essential state vector together with a ... More


Probability Distributions on Hilbert Space

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.05
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter characterizes the statistical properties of a quantum mechanical ensemble in terms of a density matrix. However, if selective measurements of one or several observables are carried out ... More


Maximum likelihood estimation of parameters

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0007
Subject:
Mathematics, Probability / Statistics

This chapter discusses maximum likelihood estimation of parameters both for the case where the distribution of the initial state vector is known and for the case where at least some elements of the ... More


Initialisation of filter and smoother

J. Durbin and S.J. Koopman

in Time Series Analysis by State Space Methods: Second Edition

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199641178
eISBN:
9780191774881
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641178.003.0005
Subject:
Mathematics, Probability / Statistics

Computational algorithms in state space analyses are mainly based on recursions, that is, formulae in which the value at time t + 1 is calculated from earlier values for t, t − 1, …, 1. This chapter ... More


Dirac, Von Neumann, and the Derivation of the Quantum Formalism: State Vectors in Hilbert Space

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/9780198827856.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The evolution of quantum mechanics through the 1920s was profoundly messy. Some physicists believed that it was necessary to throw out much of the conceptual baggage that early quantum mechanics ... More


New Design Rules for Quantum: The Postulates

Duncan G. Steel

in Introduction to Quantum Nanotechnology: A Problem Focused Approach

Published in print:
2021
Published Online:
July 2021
ISBN:
9780192895073
eISBN:
9780191924149
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780192895073.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

In the previous six chapters, we focused on understanding the basic eigenstates of various Hamiltonians by solving the time independent Schrödinger equation. While the Hamiltonians seemed relatively ... More


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