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Essential Quantum Mechanics

Gary Bowman

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228928
eISBN:
9780191711206
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228928.001.0001
Subject:
Physics, Condensed Matter Physics / Materials

Quantum mechanics — central not only to physics, but also to chemistry, materials science, and other fields — is notoriously abstract and difficult. This book is a concise, explanatory book that ... More


One-dimensional motion

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/9780199232710.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter analyzes problems that deal with stationary states in the discrete spectrum; the Schrödinger equation in momentum space (the Green function and integral form of the Schrödinger ... More


Stochastic Dynamics In Hilbert Space

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.06
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter contains the foundations of the stochastic formulation of continuous measurements carried out on an open quantum system. It shows that the time evolution of the state vector, conditioned ... More


Review of quantum mechanics

Alan Corney

in Atomic and Laser Spectroscopy

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199211456
eISBN:
9780191705915
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211456.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter derives the quantum mechanical wave functions which describe the energy levels of simple atoms. Schrödinger's equation is introduced as well and the angular part of the equation is ... More


The Development of the Quantum 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/9780198240686.003.0013
Subject:
Philosophy, Philosophy of Mind, Metaphysics/Epistemology

One way in which the quantum mechanical state of a particle can change is by measurement According to the quantum theory, when an observable of a particle is precisely measured, the state of that ... More


Many Worlds?: Everett, Quantum Theory, and Reality

Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace (eds)

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199560561
eISBN:
9780191721380
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199560561.001.0001
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

What does realism about the quantum state imply? What follows when quantum theory is applied without restriction, if need be, to the whole universe? These are the questions which are debated in this ... 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

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


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


The Schrödinger Equation in the Presence of Fields

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/9780199575398.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter derives the Hamiltonian for the electronic Schrödinger equation of a molecule in the presence of external and internal static electric or magnetic fields. It starts off with the ... More


Time Evolution

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/9780199228928.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

The time-dependent Schrödinger equation forms the chapter's starting point. For a time-independent Hamiltonian, a quantum state may be time evolved with the standard, unitary time evolution operator. ... More


Schrödinger equation on a lattice

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/9780198749349.003.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter begins by studying the one-dimensional time-dependent Schrödinger equation. In order to do this the chapter discretizes the spatial coordinates, and thus the differential equation ... More


Hamilton–Jacobi theory

S. G. Rajeev

in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199670857
eISBN:
9780191775154
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199670857.003.0009
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter derives the Hamilton-Jacobi equation. Euler's two centre problem is solved by using separation of variables in the elliptical co-ordinate system. The connection to the eikonal equation ... More


The Quantum Postulates

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/9780199228928.003.0002
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the concept of a postulate and develops the basic structure of quantum mechanics using three postulates. Postulate 1 introduces the concept of a quantum state as a solution of ... More


Quantum Mechanics

Nicholas Manton and Nicholas Mee

in The Physical World: An Inspirational Tour of Fundamental Physics

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198795933
eISBN:
9780191837111
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198795933.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

In this chapter, the main features of quantum theory are presented. The chapter begins with a historical account of the invention of quantum mechanics. The meaning of position and momentum in quantum ... More


The Stochastic Simulation Method

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.07
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The formulation of the dynamics of open quantum systems by means of stochastic processes in Hilbert space leads to efficient Monte–Carlo simulation techniques which are introduced and examined in ... More


Potential energy surfaces

Niels E. Henriksen and Flemming Y. Hansen

in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199203864
eISBN:
9780191708251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199203864.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses potential energy surfaces, that is, the electronic energy as a function of the internuclear coordinates as obtained from the electronic Schrödinger equation. It focuses on the ... 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


Practical Quantum Mechanics: Modern Tools and Applications

Efstratios Manousakis

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

The book contains lectures notes for a graduate two-semester course in quantum mechanics. It differs from other quantum mechanics textbooks as various parts of the book are inspired by rather recent ... More


Radiation in Classical and Quantal Atoms

Weiner John and Frederico Nunes

in Light-Matter Interaction: Physics and Engineering at the Nanoscale

Published in print:
2012
Published Online:
December 2013
ISBN:
9780198567653
eISBN:
9780191775147
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567653.003.0008
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter begins with a discussion of radiation by a microscopic classical oscillator with radiative damping. It then turns to the Schrödinger equation for the hydrogen atom, and an extended ... More


Introduction

Niels E. Henriksen and Flemming Y. Hansen

in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199203864
eISBN:
9780191708251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199203864.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized ... More


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