## 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:
- February 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: 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

## 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

*M. Suhail Zubairy*

### in Quantum Mechanics for Beginners: With Applications to Quantum Communication and Quantum Computing

- Published in print:
- 2020
- Published Online:
- June 2020
- ISBN:
- 9780198854227
- eISBN:
- 9780191888649
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198854227.003.0017
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

In this chapter, the Schrödinger equation is “derived” for particles that can be described by de Broglie waves. The Schrödinger equation is very different from the corresponding equation of motion in ... 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:
- February 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

## Schrödinger’s Derivation of the Wave Equation: Quantization as an Eigenvalue Problem

*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/9780198827856.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Bohr’s theory of the atom was in trouble as soon as it was formulated. Further detailed spectroscopy studies encouraged a proliferation of quantum numbers and ‘selection rules’ in what became known ... 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