Modern quantum theory : from quantum mechanics to entanglement and quantum information / Reinhold Bertlmann and Nicolai Friis.

Format:

Book

Author/Creator:

Bertlmann, Reinhold A., author.

Friis, Nicolai, author.

Language:

English

Subjects (All):

Quantum theory.

Physical Description:

1 online resource (1028 pages)

Other Title:

Modern Quantum Theory

Place of Publication:

Oxford : Oxford University Press, [2023]

Summary:

Aimed at university students, as well as academic and industry researchers, this textbook is an introduction to quantum theory, covering the development of the field from the early stages of quantum mechanics to modern quantum information, with a focus on entanglement theory.

Contents:

Intro

Title Page

Copyright Page

Dedication

Acknowledgements

Preface

Content

Part I Quantum Mechanics

1 Wave-Particle Duality

1.1 Planck's Law of Black-Body Radiation

1.1.1 Quantization of Energy

1.1.2 Black-Body Radiation

1.1.3 Derivation of Planck's Law

1.2 The Photoelectric Effect

1.2.1 Observation of the Photoelectric Effect

1.2.2 Einstein's Explanation for the Photoelectric Effect

1.2.3 The Millikan Experiment

1.3 The Compton Effect

1.3.1 The Compton Shift Formula

1.3.2 The Experiment of Compton

1.4 Bohr's Theses

1.5 Wave Properties of Matter

1.5.1 Louis de Broglie's Hypothesis

1.5.2 Electron Diffraction from a Crystal

1.6 Heisenberg's Uncertainty Principle

1.6.1 Heisenberg's Microscope

1.6.2 Energy-Time Uncertainty Principle

1.7 The Double-Slit Experiment

1.7.1 Comparison of Classical and Quantum-Mechanical Results

1.7.2 Interpretation of Quantum-Mechanical Results

1.7.3 Interferometry with Large Molecules

1.8 Schrödinger's Cat

2 The Time-Dependent Schrödinger Equation

2.1 Wave Function and Time-Dependent Schrödinger Equation

2.1.1 Discovering the Schrödinger Equation

2.1.2 First Quantization

2.1.3 The Interpretation of the Wave Function

2.1.4 The Normalization of the Wave Function

2.2 The Continuity Equation

2.3 States and Observables

2.3.1 The Scalar Product

2.3.2 Operators

2.3.3 The Commutator

2.4 Expectation Values and Variances

2.4.1 Expectation Values of Operators

2.4.2 Uncertainty of Observables

2.5 The Uncertainty Principle

2.5.1 Uncertainty Relation for Observables

2.5.2 Position-Momentum Uncertainty

2.5.3 Uncertainty of Gaussian Wave Packets

2.5.4 Wave Packets in Momentum Space

2.6 Time Evolution in Quantum Mechanics

2.6.1 The Propagator.

2.6.2 Schrödinger Picture and Heisenberg Picture

2.6.3 Time Evolution of Expectation Values

2.6.4 Time Evolution of Free Wave Packets

2.6.5 Energy-Time Uncertainty

2.7 Recovering Classical Physics

2.7.1 The Ehrenfest Theorem

2.7.2 Dirac's Rule

3 Mathematical Formalism of Quantum Mechanics

3.1 Hilbert Space

3.1.1 Norm and Completeness

3.1.2 Dimensionality of Hilbert Spaces

3.1.3 The Dual Hilbert Space and Dirac Notation

3.1.4 The Hilbert Space for Photon Polarization

3.2 Operators on Finite-Dimensional Hilbert Spaces

3.2.1 Projectors

3.2.2 The Spectral Theorem

3.2.3 Unitary Operators

3.3 Infinite-Dimensional Hilbert Spaces

3.3.1 Self-adjoint Operators on Infinite-Dimensional Hilbert Spaces

3.3.2 Continuous Spectra

3.3.3 Distributional Aspects of Quantum Mechanics

4 The Time-Independent Schrödinger Equation

4.1 Solving the Schrödinger Equation

4.1.1 Stationary States

4.1.2 The Schrödinger Equation as an Eigenvalue Problem

4.1.3 Expansion into Stationary States

4.1.4 Physical Interpretation of the Expansion Coefficients

4.2 Bound States

4.2.1 The Finite Potential Well

4.2.2 The Infinite Potential Well

4.2.3 The Dirac-Delta Potential Well

4.2.4 The Double Well and the Ammonia Molecule

4.3 Scattering and the Tunnel Effect

4.3.1 The Finite Potential Barrier

4.3.2 Reflection and Transmission

4.3.3 Tunnelling and the Gamow Factor

4.3.4 Transmission Resonances

5 The Quantum Harmonic Oscillator

5.1 Algebraic Method

5.1.1 Annihilation and Creation Operators

5.1.2 The Occupation-Number Operator

5.1.3 The Ground State of the Harmonic Oscillator

5.1.4 Eigenstates of the Harmonic Oscillator

5.2 Analytic Method

5.2.1 The Differential Equation of the Harmonic Oscillator

5.2.2 The Hermite Polynomials

5.3 Zero-Point Energy.

5.3.1 Uncertainty Relation for the Harmonic Oscillator

5.3.2 The Zero-Point Energy of the Harmonic Oscillator

5.4 Comparison with the Classical Oscillator

5.5 The Three-Dimensional Harmonic Oscillator

5.5.1 Eigenstates of the Three-Dimensional Harmonic Oscillator

5.5.2 Systems of Multiple Degrees of Freedom

6 Orbital Angular Momentum

6.1 Angular Momentum and the Rotation Group

6.1.1 The Orbital Angular Momentum Operator

6.1.2 The Rotation Group in Three Dimensions

6.1.3 Lie Groups and Lie Algebras

6.2 Rotations in the Hilbert Space

6.2.1 Unitary Representations of the Rotation Group

6.2.2 The Lie Algebra of the Rotation Group

6.2.3 Rotation of the Wave Function

6.2.4 Rotation of Operators

6.2.5 Rotation of Vector Operators

6.2.6 Rotation of Scalar Operators

6.3 Angular Momentum Eigenstates and Eigenvalues

6.3.1 Angular Momentum Ladder Operators

6.3.2 Angular Momentum Eigenvalues

6.3.3 Angular Momentum Eigenstates

6.4 Angular Momentum Eigenfunctions

6.4.1 Spherical Polar Coordinates

6.4.2 Angular Momentum Operators in Spherical Coordinates

6.4.3 The Spherical Harmonics

6.4.4 Uncertainty of Angular-Momentum Operators

7 The Three-Dimensional Schrödinger Equation

7.1 The Radial Schrödinger Equation

7.1.1 Angular Momentum in the Schrödinger Equation

7.1.2 Reduced Wave Function and Effective Potential

7.2 Bound States in Three Dimensions

7.2.1 Normalization of the Radial Wave Function

7.2.2 Rayleigh-Ritz Variational Principle

7.3 The Spherical Potential Well

7.3.1 General Solutions for the Spherical Potential Well

7.3.2 The Ground State of the Spherical Potential Well

7.4 The Coulomb Potential and the Stability of Matter

7.4.1 The Coulomb Potential

7.4.2 An Upper Bound on the ground-state energy of the H-Atom.

7.4.3 A Lower Bound from Heisenberg's Uncertainty

7.4.4 A Lower Bound: Sobolev Inequalities

7.5 The Hydrogen Atom

7.5.1 The Radial Schrödinger Equation for the Hydrogen Atom

7.5.2 The Energy Levels of the Hydrogen Atom

7.5.3 The Laguerre Polynomials

7.5.4 Properties of the Hydrogen Atom

8 Spin and Atomic Structure

8.1 The Magnetic Dipole Moment

8.1.1 Classical Magnetic Dipoles

8.1.2 The Magnetic Dipole Moment of the Hydrogen Atom

8.1.3 Magnetic Dipoles in External Magnetic Fields

8.2 Spin

8.2.1 The Stern-Gerlach Experiment

8.2.2 Spin 1/2

8.2.3 Mathematical Formulation of Spin

8.2.4 Spin Measurements

8.2.5 Spinors and the Relation of SO(3) and SU(2)

8.3 The Atomic Structure-Revisited

8.3.1 Total Angular Momentum

8.3.2 Addition of Angular Momenta

8.3.3 Indistinguishable Particles and Pauli Principle

8.3.4 Electronic Orbitals

8.3.5 Term Symbols and Hund's Rules

9 Electromagnetism in Quantum Mechanics

9.1 The Pauli Equation

9.1.1 Hamiltonian for the Interaction with the Electromagnetic Field

9.1.2 Paramagnetic and Diamagnetic Contributions

9.1.3 The Stern-Gerlach Term

9.2 Gauge Symmetries in Quantum Mechanics

9.3 The Aharonov-Bohm effect

9.4 Geometric Phases

9.4.1 Holonomy

9.4.2 The Berry Phase

9.4.3 The Aharonov-Anandan Phase

9.4.4 Spin 1/2 in Adiabatically Rotating Magnetic Field

9.5 A Rush through Differential Geometry and Topology

9.5.1 Differential Geometry

9.5.2 Fibre Bundles

9.5.3 Connection and Curvature

9.6 Topological Interpretation of Physical Effects

9.6.1 Aharonov-Bohm Effect and Topology

9.6.2 Berry Phase and Topology

9.6.3 Dirac Monopole and Topology

10 Perturbative Methods in Quantum Mechanics

10.1 Time-Independent Perturbation Theory

10.1.1 Rayleigh-Schrödinger Perturbation Theory.

10.1.2 Non-Degenerate Perturbation Theory

10.1.3 Degenerate Perturbation Theory

10.1.4 Avoided Crossings

10.2 The Fine Structure of the Hydrogen Atom

10.2.1 Relativistic Correction to the Kinetic Energy

10.2.2 Spin-Orbit Correction

10.2.3 The Darwin Correction

10.2.4 Combined Fine-Structure Correction

10.3 The Zeeman Effect

10.3.1 Weak Field-Anomalous Zeeman Effect

10.3.2 Strong Field-Paschen-Back Effect

10.4 The Stark Effect for the Hydrogen Atom

10.4.1 The Wigner-Eckart Theorem

10.4.2 First-Order Stark Effect

10.4.3 Second-Order Stark Effect

10.5 Time-Dependent Perturbation Theory

10.5.1 Time-Dependent Hamiltonians

10.5.2 The Interaction Picture

10.5.3 Fermi's Golden Rule

Part II Entanglement and Non-Locality

11 Density Matrices

11.1 Pure States

11.2 Mixed States

11.3 Time Evolution of Density Matrices

11.4 Density Matrices for Quantum Systems in Thermal Equilibrium

11.5 Density Matrices for Two-Level Quantum Systems

11.5.1 Pure and Mixed States of a Single Qubit

11.5.2 The Bloch Decomposition

11.5.3 Spin 1/2 in an External Magnetic Field

11.6 Geometry of the State Space

11.7 Density Matrices for Bipartite Quantum Systems

12 Hidden-Variable Theories

12.1 Historical Overview and Hidden-Variable Basics

12.2 Von Neumann and Additivity of Measurement Values

12.2.1 Von Neumann's Assumption

12.2.2 Bell's Two-Dimensional Hidden-Variable Model

12.3 Contextuality

12.4 Statements Incompatible with Quantum Mechanics

12.5 The Kochen-Specker Theorem

12.5.1 Kochen-Specker Theorem for Spin-1 System

12.5.2 Peres' Nonet for Two Qubits

12.5.3 Mermin's Pentagram for Three Qubits

13 Bell Inequalities

13.1 The EPR Paradox

13.1.1 The EPR Criteria

13.1.2 The EPR Paradox-Aharonov-Bohm Scenario

13.1.3 Bohr's Reply to EPR

13.1.4 Schrödinger's Reply to EPR.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-19-150634-6

0-19-199748-X