Modern Quantum Physics: A Practical Applications Approach
- Length: 280 pages
- Edition: 1
- Language: English
- Publisher: Iop Publishing Ltd
- Publication Date: 2022-02-28
- ISBN-10: 0750321652
- ISBN-13: 9780750321655
- Sales Rank: #1937845 (See Top 100 Books)
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. These include a mathematically sound treatment of delta functions and the rigged Hilbert space, an exposition of many-body theory including density functional theory and Feynman diagrams, and an explanation of chemical bonds and energy band theory. It also contains expansive chapters on relativistic Dirac theory, group theory including Lie groups, exotic quantum phenomena, interpretations of quantum theory, quantum computers and quantum cryptography. Each chapter ends with a set of questions and exercises for the student. This authoritative and expansive survey of the field is ideal for advanced researchers, upper undergraduate and graduate studentss, with a main purpose as a text for a graduate course in quantum mechanics.
Key features
- Provides a thorough review of the basics
- Discusses the philosophical questions of quantum theory
- Includes the concepts used in quantum condensed matter physics and quantum chemistry in detail
- Presents quantum information
Cover Title Copyright Contents Preface Acknowledgement Author biography 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 Problems References 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 Problems References 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 Problems References 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 Problems References 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 Problems References 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 Problems References 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 Problems Reference 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 8.9.1 First experiment 8.9.2 Quarter-wave plate 8.9.3 Second experiment 8.9.4 Third experiment 8.9.5 Fourth experiment 8.10 Resume Problems References 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 Problems References 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 Problems Reference 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 Problems References 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 Problems References
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