Modern quantum mechanics and quantum information / J.S. Faulkner.

Format:

Book

Author/Creator:

Faulkner, J. S., author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP ebooks. 2021 collection.

IOP ebooks. [2021 collection]

Language:

English

Subjects (All):

Quantum theory.

Physical Description:

1 online resource (various pagings) : illustrations (some color).

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Biography/History:

Prof. John Samuel (Sam) Faulkner was born in Memphis, Tennessee. He obtained BS and MS degrees in physics from Auburn University. He was awarded a PhD in physics by The Ohio State University. He has published over 86 journal articles in the area of theoretical condensed matter physics.

Summary:

Modern Quantum Mechanics and Quantum Information surveys the fundamental aspects of quantum mechanics against the backdrop of its use in modern science applications. The book covers several topics in modern quantum mechanics and quantum information that do not appear in older texts.

Contents:

1. Review of basics

1.1. About quantum mechanics

1.2. Hilbert space

1.3. Elementary quantum mechanics

1.4. Dirac and von Neumann

1.5. Rigged Hilbert space

1.6. Observables and Hermitean operators

1.7. The uncertainty relation

1.8. Commuting observables

1.9. Unitary operators

1.10. The Gaussian wave packet

1.11. Two-dimensional Hilbert space

1.12. Pairs of spins

1.13. Einstein, Podolsky, and Rosen

2. Non-relativistic quantum mechanics

2.1. Heisenberg's matrix mechanics

2.2. The one-dimensional harmonic oscillator

2.3. Schrödinger's wave mechanics

2.4. The one-dimensional harmonic oscillator (again)

2.5. Comparison of Heisenberg and Schrödinger theories

2.6. Wave mechanics in three dimensions

2.7. Angular momentum

2.8. Schrödinger equation for a spherically symmetric potential

2.9. Schrödinger equation for the hydrogen atom

2.10. Time-dependent wave equation

2.11. The time-evolution operator

2.12. The time dependence of Heisenberg's operators

3. Relativistic quantum mechanics

3.1. The necessity for relativistic quantum mechanics

3.2. Klein-Gordon equation

3.3. Problems with the Klein-Gordon equation

3.4. Dirac theory

3.5. Proof of the Lorentz covariance of the Dirac equation

3.6. The fifth gamma matrix

3.7. Free particle solution of the Dirac equation

3.8. Angular momentum and spin

3.9. The magnetic moment of the electron

3.10. Scalar relativistic approximation

3.11. The Dirac theory of the hydrogen atom

3.12. Advantages and disadvantages

4. Symmetry

4.1. The importance of symmetry in physics

4.2. A simple example

4.3. Theory of finite groups

4.4. Representations of finite groups

4.5. Theory of infinite groups and Lie groups

4.6. Continuous groups in physics

4.7. Conservation laws from Noether's theorem

4.8. Conservation laws from quantum mechanics

4.9. Continuous group representations

4.10. Groups of a Hamiltonian

4.11. Conclusions

5. Approximate methods

5.1. Rayleigh-Ritz variational method

5.2. Time-independent perturbation theory

5.3. Time-dependent perturbation theory

5.4. The two-level Hamiltonian

5.5. Spin magnetic resonance

5.6. The maser

5.7. Fermi's golden rule

5.8. An atom interacting with a plane electromagnetic wave

5.9. Approximate methods that use computers

6. Scattering and Green's functions

6.1. Potential scattering

6.2. Position representation

6.3. The spherical scatterer

6.4. The optical theorem

6.5. The Born approximation

6.6. Green's function and its adjoint

6.7. Green's function with a scatterer

6.8. The non-spherical scattering potential with bounded domain

6.9. Spectral theory from scattering theory

6.10. Krein's theorem

7. A practical tool

7.1. The exact equations

7.2. Pauli exclusion principle

7.3. Atomic structure

7.4. The hydrogen molecule

7.5. Covalent bonding

7.6. Ionic bonding

7.7. Bonding in metals

7.8. Conclusions

8. An alternative reality

8.1. Gazing in wonder

8.2. The Einstein-Podolsky-Rosen experiment

8.3. Hidden variables

8.4. Bell's inequalities

8.5. Double slit interference

8.6. The adiabatic theorem

8.7. The Bohm-Aharanov phase

8.8. The Berry phase

8.9. Quantum erasure

8.10. Resume

9. What does it all mean?

9.1. What are we to make of quantum experiments?

9.2. The Orthodox Copenhagen interpretation (Bohr)

9.3. Bohm's interpretation

9.4. The many-worlds interpretation

9.5. The Ghirardi-Rimini-Weber (GRW) interpretation

9.6. Consistent (decoherent) histories interpretation

9.7. Most widely held interpretation

9.8. Decoherence

9.9. Density matrices

9.10. Defining decoherence

9.11. Simple example of decoherence

9.12. Back to Schrödinger's cat

10. Quantum information

10.1. Information science

10.2. Turing machine

10.3. Bits and bytes and Boolean gates

10.4. Universality

10.5. Measuring information

10.6. Landauer's theory of the energy required for calculations

10.7. Reversible computing

10.8. Universality

10.9. Zero power computing

10.10. Computational complexity

10.11. Quantum devices

10.12. Quantum bits (qubits)

10.13. Single qubit gates

10.14. Random number generator

10.15. A two qubit gate

10.16. No cloning theorem

10.17. Bell or EPR states

10.18. Entanglement and disentanglement

10.19. Quantum teleportation

10.20. Superdense coding

10.21. Deutsch's algorithm

10.22. Deutsch-Jozsa algorithm

10.23. Four-level Deutsch-Jozsa experiment

10.24. Discrete Fourier transform

10.25. The quantum Fourier transform

11. Quantum cryptography

11.1. The Caesar cipher

11.2. Symmetric key cryptography

11.3. Public-key cryptography (asymmetric cryptography)

11.4. Modular arithmetic

11.5. RSA public key system. Rivest, Shamir, Adleman

11.6. Diffie-Hellman key exchange

11.7. Discrete logarithm problem

11.8. ElGamal

11.9. Elliptic curves

11.10. The Vernam cipher

11.11. Quantum key distribution

11.12. Shor factoring algorithm

12. Many particle systems

12.1. The Schrödinger equation

12.2. Hartree theory

12.3. Hartree-Fock theory

12.4. Configuration interaction (CI) calculations

12.5. The electron gas in the Hartree-Fock approximation

12.6. Critique of the H-F approximation

12.7. Density matrices

12.8. Single configuration approximation

12.9. The Thomas-Fermi and Thomas-Fermi-Dirac theories

12.10. The density functional theory (DFT)

12.11. The local density approximation (LDA)

12.12. Beyond the density functional theory

12.13. Infinite-order perturbation theory and Feynman diagrams

12.14. Dielectric function of a degenerate electron gas

12.15. Progress requires cooperation.

Notes:

"Version: 202112"--Title page verso.

Includes bibliographical references.

Title from PDF title page (viewed on January 18, 2022).

ISBN:

0-7503-2166-0

0-7503-2167-9

OCLC:

1294828726