Modern quantum mechanics and quantum information /

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"Version: 202112"--Title page verso.Includes bibliographical references.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 Rosen2. Non-relativistic quantum mechanics -- 2.1. Heisenberg's matrix mechanics -- 2.2. The one-dimensional harmonic oscillator -- 2.3. Schr?odinger's wave mechanics -- 2.4. The one-dimensional harmonic oscillator (again) -- 2.5. Comparison of Heisenberg and Schr?odinger theories -- 2.6. Wave mechanics in three dimensions -- 2.7. Angular momentum -- 2.8. Schr?odinger equation for a spherically symmetric potential -- 2.9. Schr?odinger 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 operators3. 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 disadvantages4. 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. Conclusions5. 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 computers6. 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 theorem7. 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. Conclusions8. 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. Resume9. 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 Schr?odinger's cat10. 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 transform11. 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 algorithm12. Many particle systems -- 12.1. The Schr?odinger 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 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.Upper level undergrad/graduate.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.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.Title from PDF title page (viewed on January 18, 2022).

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

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English

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9780750321679

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530.12

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Quantum theory.
Quantum science.

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J.S. Faulkner.

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