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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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