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Quantum Theory: A Wide Spectrum

Posted By: Culin
Quantum Theory: A Wide Spectrum

Quantum Theory: A Wide Spectrum
E.B. Manoukian | Springer | 1rst edition (November 20, 2006) | ISBN-10: 1402041896 | PDF | 10 Mb | 1011 Pages




Description:

The ultimate modern textbook on Quantum Theory, this graduate-level and self-contained s text is also a reference and research work which provides background for researchers in this discipline, covering important recent developments and most aspects of the theory with fairly detailed presentations.
In addition to traditional topics, it includes: selective measurements, Wigner's Theorem of symmetry transformations, generators of quantum transformations, supersymmetry, details on the spectra of Hamiltonians and stability of quantum systems, Bose-Fermi oscillators, coherent states, hyperfine structure of the H-atom for any angular momentum, the non-relativistic Lamb shift, anomalous magnetic moment of the electron, Ramsey oscillatory fields methods, measurement, interference and the role of the environment, the AB effect, geometric phases (including the nonadiabatic and noncyclic), Schrödinger's cat and quantum decoherence, quantum teleportation and cryptography, quantum dynamics of the Stern-Gerlach effect, Green functions, path integrals, including constrained dynamics, quantum dynamical principle and variations, systematics of multi-electron atoms, stability of matter, collapse of "bosonic matter" and the role of spin, intricacies of scattering, quantum description of relativistic particles for any spin and mass, spinors, helicity, the Spin & Statistics Theorem.
In addition it contains numerous problems, some of which are challenging enough for research.

Table of contents:

Preface. Acknowledgments.
1: Fundamentals. 1.1 Selective Measurements 1.2. A, B, C to Probabilities. 1.3. Expectation Values and Matrix Representations. 1.4. Generation of States, Inner-Product Spaces, Hermitian Operators and the Eigenvalue Problem. 1.5. Pure Ensembles and Mixtures 1.6. Polarization of Light: An Interlude. 1.7. The Hilbert Space; Rigged Hilbert Space. 1.8. Self-Adjoint Operators and Their Spectra. 1.9. Wigner’s Theorem on Symmetry Transformations. 1.10. Probability, Conditional Probability and Measurement. Problems.
2: Symmetries and Transformations. 2.1. Galilean Space-Time Coordinate Transformations. 2.2. Successive Galilean Transformations and the Closed Path. 2.3. Quantum Galilean Transformations and Their Generators. 2.4. The Transformation Function (x|p). 2.5. Quantum Dynamics and Construction of Hamiltonians. Appendix to §2.5: Time-Evolution for Time-Dependent Hamiltonians. 2.6. Discrete Transformations: Parity and Time Reversal. 2.7. Orbital Angular Momentum and Spin. 2.8. Spinors and Arbitrary Spins. Appendix to §2.8: Transformation Rule of a Spinor of Rank One Under a Coordinate Rotation. 2.9. Supersymmetry. Problems.
3: Uncertainties, Localization, Stability and Decay of Quantum Systems. 3.1. Uncertainties, Localization and Stability. 3.2. Boundedness of the Spectra of Hamiltonians From Below. 3.3. Boundedness of Hamiltonians From Below: General Classes of Interactions. 3.4. Boundedness of Hamiltonian From Below: Multi-Particle Systems. 3.5. Decay of Quantum Systems. Appendix to §3.5: The Paley-Wiener Theorem. Problems.
4: Spectra of Hamiltonians. 4.1. Hamiltonians with Potentials Vanishing at Infinity. 4.2. On Bound-States. 4.3. Hamiltonians with Potentials Approaching Finite Constants at Infinity. 4.4. Hamiltonians with Potentials Increasing with No Bound at Infinity. 4.5. Counting the Number of Eigenvalues. Appendix to §4.5: Evaluation of Certain Integrals. 4.6. Lower Bounds to the Expectation Value of the Kinetic Energy: An Application of Counting Eigenvalues. 4.7. The Eigenvalue Problem and Supersymmetry. Problems.
5: Angular Momentum Gymnastics. 5.1. The Eigenvalue Problem. 5.2. Matrix Elements of Finite Rotations. 5.3. Orbital Angular Momentum. 5.4. Spin. 5.5. Addition of Angular Momenta. 5.6. Explicit Expression for the Clebsch-Gordan Coefficients. 5.7. Vector Operators. 5.8. Tensor Operators. 5.9. Combining Several Angular Momenta: 6-j and 9-j Symbols. 5.10. Particle States and Angular Momentum; Helicity States. Problems.
6: Intricacies of Harmonic Oscillators. 6.1. The Harmonic Oscillator. 6.2 Transition to and Between Excited States in the Presence of a Time-Dependent Disturbance. 6.3. The Harmonic Oscillator in the Presence of a Disturbance at Finite Temperature. 6.4. The Fermi Oscillator. 6.5. Bose-Fermi Oscillators and Supersymmetric Bose-Fermi Transformations. 6.6. Coherent State of the Harmonic Oscillator. Problems.
7: Intricacies of the Hydrogen Atom. 7.1. Stability of the Hydrogen Atom. 7.2. The Eigenvalue Problem. 7.3. The Eigenstates. 7.4. The Hydrogen Atom Including Spin and Relativistic Corrections. Appendix to §7.4: Normalization of the Wavefunction Including Spin and Relativistic Corrections. 7.5. The Fine-Structure of the Hydrogen Atom. Appendix to §7.5: Combining Spin and Angular Momentum in the Atom. 7.6. The Hyperfine-Structure of the Hydrogen Atom. 7.7. The Non-Relativistic Lamb Shift. Appendix to §7.7: Counter-Terms and Mass Renormalization. 7.8. Decay of Excited States. 7.9. The Hydrogen Atom in External Electromagnetic Fields. Problems.
8: Quantum Physics of Spin 1/2 and Two-Level Systems; Quantum Predictions Using Such Systems. 8.1. General Properties of Spin 1/2 and Two-Level Systems. 8.2. The Pauli Hamiltonian; Supersymmetry. 8.3. Landau Levels; Expression for the g-Factor. 8.4. Spin Precession and Radiation Losses. 8.5. Anomalous Magnetic Moment of the Electron. 8.6. Density Operators and Spin. 8.7 Quantum Interference and Measurement; The Role of the Environment. 8.8. Ramsey Oscillatory Fields Method and Spin Flip; Monitoring the Spin. 8.9 Schrödinger’s Cat and Quantum Decoherence. 8.10. Bell’s Test. Appendix to §8.10. Entangled States; The C-H Inequality. 8.11. Quantum Teleportation and Quantum Cryptography. 8.12. Rotation of a Spinor. 8.13. Geometric Phases. 8.14. Quantum Dynamics of the Stern-Gerlach Effect. Appendix to §8.14: Time Evolution and Intensity Distribution. Problems.
9: Green Functions. 9.1. The Free Green Functions. 9.2. Linear and Quadratic Potentials. 9.3. The Dirac Delta Potential. 9.4. Time-Dependent Forced Dynamics. 9.5. The Law of Reflection and Reconciliation with the Classical Law. 9.6. Two-Dimensional Green Function in Polar Coordinates: Application to the Aharonov-Bohm Effect. 9.7. General Properties of the Full Green Functions and Applications. 9.8. The Thomas-Fermi Approximation and Deviations Thereof . 9.9. The Coulomb Green Function: The Full Spectrum.
10: Path Integrals. 10.1. The Free Particle. 10.2. Particle in a Given Potential. 10.3. Charged Particle in External Electromagnetic Fields: Velocity Dependent Potentials. 10.4. Constrained Dynamics. 10.5. Bose Excitations. 10.6. Grassmann Variables: Fermi Excitations. Problems.
11: The Quantum Dynamical Principle. 11.1. The Quantum Dynamical Principle. 11.2. Expressions for Transformations Functions. 11.3. Trace Functionals. 11.4. From the Quantum Dynamical Principle to Path Integrals. 11.5. Bose/Fermi Excitations. 11.6. Closed-Time Path and Expectation-Value Formalism. Problems.
12: Approximating Quantum Systems. 12.1. Non-Degenerate Perturbation Theory. 12.2. Degenerate Perturbation Theory. 12.3. Variational Methods. 12.4. High-Order Perturbations, Divergent Series; Padé Approximants. 12.5. WKB Approximation. 12.6. Time-Dependence; Sudden Approximation and the Adiabatic Theorem. 12.7. Master Equation; Exponential Law, Coupling to the Environment. Problems.
13: Multi-Electron Atoms: Beyond the Thomas-Fermi Atom. 13.1. The Thomas-Fermi Atom. Appendix A To §13.1: The TF Energy Gives the Leading Contribution to E(Z) for Large Z. Appendix B to §13.1: The TF Density Actually Gives the Smallest Value for the Energy Density Functional in (13.1.6). 13.2. Correction due to Electrons Bound Near the Nucleus. 13.3. The Exchange Term. 13.4. Quantum Correction. 13.5. Adding Up the Various Contributions: Estimation of E(Z). Problems.
14: Quantum Physics and the Stability of Matter. 14.1. Lower Bound to the Multi-Particle Repulsive Coulomb Potential Energy. Appendix to §14.1: A Thomas-Fermi-Like Energy Functional and No Binding. 14.2. Lower and Upper Bounds for the Ground-State Energy and the Stability of Matter. 14.3. Investigation of the High-Density Limit for Matter and Its Stability. 14.4. The Collapse of "Bosonic Matter". Appendix to §14.4: Upper Bounds for hH1i in (14.4.47). Problems.
15: Quantum Scattering. 15.1. Interacting States and Asymptotic Boundary Conditions. 15.2. Particle Detection and Connection between Configuration and Momentum Spaces in Scattering. Appendix to §15.2: Some Properties of F (u, v), 15.3. Differential Cross Sections. 15.4. The Optical Theorem and Its Interpretation; Phase Shifts. 15.5. Coulomb Scattering. 15.6. Functional Treatment of Scattering Theory. 15.7. Scattering at Small Deflection Angles at High Energies: Eikonal Approximation. 15.8. Multi-Channel Scatterings of Clusters and Bound Systems. 15.9. Passage of Particles through Media; Neutron Interferometer. Problems.
16: Quantum Description of Relativistic Particles. 16.1. The Dirac Equation and Pauli’s Fundamental Theorem. Appendix to §16.1: Pauli’s Fundamental Theorem. 16.2. Lorentz Covariance, Boosts and Spatial Rotations. 16.3. Spin, Helicity and P, C, T Transformations. 16.4. General Solution of the Dirac Equation. 16.5. Massless Dirac Particles. 16.6. Physical Interpretation, Localization and Particle Content. Appendix to §16.6: Exact Treatment of the Dirac Equation in the Bound Coulomb Problem. 16.7. The Klein-Gordon Equation. 16.8. Relativistic Wave Equations for Any Mass and Any Spin. 16.9. Spin & Statistics. Appendix to §16.9: The Action Integral. Problems. Mathematical Appendices.
I: Variations of the Baker-Campbell-Hausdorff Formula. 1. Integral Expression for the Product of the Exponentials of Operators. 2. Derivative of the Exponential of Operator-Valued Functions. 3. The Classic Baker-Campbell-Hausdorff Formula. 4. A Modification of the Baker-Campbell-Hausdorff Formula.
II: Convexity and Basic Inequalities. 1. General Convexity Theorem. 2. Minkowski’s Inequality for Integrals. 3. Hölder’s Inequality for Integrals. 4. Young’s Inequality for Integrals.
III: The Poisson Equation in 4D. 1. The Poisson Equation. 2. Generating Function. 3. Expansion Theorem. 4. Generalized Orthogonality Relation.
References.
Index.

Thanks to todorm !!