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Modern quantum mechanics and quantum information /

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.

Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Faulkner, J. S. (Autor)
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]
Colección:	IOP (Series). Release 21. IOP ebooks. 2021 collection.
Temas:	Quantum theory. Quantum physics (quantum mechanics & quantum field theory) Quantum science.
Acceso en línea:	Texto completo

Tabla de Contenidos:

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.

Modern quantum mechanics and quantum information /

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