Limit search to available items
Book Cover
E-book
Author Razavy, Mohsen.

Title Heisenberg's quantum mechanics / Mohsen Razavy
Published Singapore ; Hackensack, N.J. : World Scientific, ©2011
Online access available from:
World Scientific    View Resource Record  

Copies

Description 1 online resource (xix, 657 pages) : illustrations
Contents Machine generated contents note: 1.1. The Lagrangian and the Hamilton Principle -- 1.2. Noether's Theorem -- 1.3. The Hamiltonian Formulation -- 1.4. Canonical Transformation -- 1.5. Action-Angle Variables -- 1.6. Poisson Brackets -- 1.7. Time Development of Dynamical Variables and Poisson Brackets -- 1.8. Infinitesimal Canonical Transformation -- 1.9. Action Principle with Variable End Points -- 1.10. Symmetry and Degeneracy in Classical Dynamics -- 1.11. Closed Orbits and Accidental Degeneracy -- 1.12. Time-Dependent Exact Invariants -- 2.1. Equivalence of Wave and Matrix Mechanics -- 3.1. Vectors and Vector Spaces -- 3.2. Special Types of Operators -- 3.3. Vector Calculus for the Operators -- 3.4. Construction of Hermitian and Self-Adjoint Operators -- 3.5. Symmetrization Rule -- 3.6. Weyl's Rule -- 3.7. Dirac's Rule -- 3.8. Von Neumann's Rules -- 3.9. Self-Adjoint Operators -- 3.10. Momentum Operator in a Curvilinear Coordinates
14.2. Two Solvable Problems -- 14.3. Time-Dependent Scattering Theory -- 14.4. The Scattering Matrix -- 14.5. The Lippmann[-]Schwinger Equation -- 14.6. Analytical Properties of the Radial Wave Function -- 14.7. The Jost Function -- 14.8. Zeros of the Jost Function and Bound Sates -- 14.9. Dispersion Relation -- 14.10. Central Local Potentials having Identical Phase Shifts and Bound States -- 14.11. The Levinson Theorem -- 14.12. Number of Bound States for a Given Partial Wave -- 14.13. Analyticity of the S-Matrix and the Principle of Casuality -- 14.14. Resonance Scattering -- 14.15. The Born Series -- 14.16. Impact Parameter Representation of the Scattering Amplitude -- 14.17. Determination of the Impact Parameter Phase Shift from the Differential Cross Section -- 14.18. Elastic Scattering of Identical Particles -- 14.19. Transition Probability -- 14.20. Transition Probabilities for Forced Harmonic Oscillator -- 15.1. Diffraction in Time -- 15.2. High Energy Scattering from an Absorptive Target
9.8. The Hydrogen Atom -- 9.9. Calculation of the Energy Eigenvalues Using the Runge[-]Lenz Vector -- 9.10. Classical Limit of Hydrogen Atom -- 9.11. Self-Adjoint Ladder Operator -- 9.12. Self-Adjoint Ladder Operator tiff Angular Momentum -- 9.13. Generalized Spin Operators -- 9.14. The Ladder Operator -- 10.1. Discrete-Time Formulation of the Heisenberg's Equations of Motion -- 10.2. Quantum Tunneling Using Discrete-Time Formulation -- 10.3. Determination of Eigenvalues from Finite-Difference Equations -- 10.4. Systems with Several Degrees of Freedom -- 10.5. Weyl-Ordered Polynomials and Bender[-]Dunne Algebra -- 10.6. Integration of the Operator Differential Equations -- 10.7. Iterative Solution for Polynomial Potentials -- 10.8. Another Numerical Method for the Integration of the Equations of Motion -- 10.9. Motion of a Wave Packet -- 11.1. Perturbation Theory Applied to the Problem of a Quartic Oscillator -- 11.2. Degenerate Perturbation Theory
3.11. Summation Over Normal Modes -- 4.1. The Uncertainty Principle -- 4.2. Application of the Uncertainty Principle for Calculating Bound State Energies -- 4.3. Time-Energy Uncertainty Relation -- 4.4. Uncertainty Relations for Angular Momentum-Angle Variables -- 4.5. Local Heisenberg Inequalities -- 4.6. The Correspondence Principle -- 4.7. Determination of the State of a System -- 5.1. Schwinger's Action Principle and Heisenberg's equations of Motion -- 5.2. Nonuniqueness of the Commutation Relations -- 5.3. First Integrals of Motion -- 6.1. Galilean Invariance -- 6.2. Wave Equation and the Galilean Transformation -- 6.3. Decay Problem in Nonrelativistic Quantum Mechanics and Mass Superselection Rule -- 6.4. Time-Reversal Invariance -- 6.5. Parity of a State -- 6.6. Permutation Symmetry -- 6.7. Lattice Translation -- 6.8. Classical and Quantum Integrability -- 6.9. Classical and Quantum Mechanical Degeneracies -- 7.1. Klein's Method -- 7.2. The Anharmonic Oscillator -- 7.3. The Double-Well Potential
7.4. Chasman's Method -- 7.5. Heisenberg's Equations of Motion for Impulsive Forces -- 7.6. Motion of a Wave Packet -- 7.7. Heisenberg's and Newton's Equations of Motion -- 8.1. Energy Spectrum of the Two-Dimensional Harmonic Oscillator -- 8.2. Exactly Solvable Potentials Obtained from Heisenberg's Equation -- 8.3. Creation and Annihilation Operators -- 8.4. Determination of the Eigenvalues by Factorization Method -- 8.5. A General Method for Factorization -- 8.6. Supersymmetry and Superpotential -- 8.7. Shape Invariant Potentials -- 8.8. Solvable Examples of Periodic Potentials -- 9.1. The Angular Momentum Operator -- 9.2. Determination of the Angular Momentum Eigenvalues -- 9.3. Matrix Elements of Scalars and Vectors and the Selection Rules -- 9.4. Spin Angular Momentum -- 9.5. Angular Momentum Eigenvalues Determined from the Eigenvalues of Two Uncoupled Oscillators -- 9.6. Rotations in Coordinate Space and in Spin Space -- 9.7. Motion of a Particle Inside a Sphere
11.3. Almost Degenerate Perturbation Theory -- 11.4. van der Waals Interaction -- 11.5. Time-Dependent Perturbation Theory -- 11.6. The Adiabatic Approximation -- 11.7. Transition Probability to the First Order -- 12.1. WKB Approximation for Bound States -- 12.2. Approximate Determination of the Eigenvalues for Nonpolynomial Potentials -- 12.3. Generalization of the Semiclassical Approximation to Systems with N Degrees of Freedom -- 12.4. A Variational Method Based on Heisenberg's Equation of Motion -- 12.5. Raleigh[-]Ritz Variational Principle -- 12.6. Tight-Binding Approximation -- 12.7. Heisenberg's Correspondence Principle -- 12.8. Bohr and Heisenberg Correspondence and the Frequencies and Intensities of the Emitted Radiation -- 13.1. Equations of Motion of Finite Order -- 13.2. Equation of Motion of Infinite Order -- 13.3. Classical Expression for the Energy -- 13.4. Energy Eigenvalues when the Equation of Motion is of Infinite Order -- 14.1. Determinantal Method in Potential Scattering
16.1. The Aharonov-Bohm Effect -- 16.2. Time-Dependent Interaction -- 16.3. Harmonic Oscillator with Time-Dependent Frequency -- 16.4. Heisenberg's Equations for Harmonic Oscillator with Time-Dependent Frequency -- 16.5. Neutron Interferometry -- 16.6. Gravity-Induced Quantum Interference -- 16.7. Quantum Beats in Waveguides with Time-Dependent Boundaries -- 16.8. Spin Magnetic Moment -- 16.9. Stern-Gerlach Experiment -- 16.10. Precession of Spin Magnetic Moment in a Constant Magnetic Field -- 16.11. Spin Resonance -- 16.12. A Simple Model of Atomic Clock -- 16.13. Berry's Phase -- 17.1. Ground State of Two-Electron Atom -- 17.2. Hartree and Hartree-Fock Approximations -- 17.3. Second Quantization -- 17.4. Second-Quantized Formulation of the Many-Boson Problem -- 17.5. Many-Fermion Problem -- 17.6. Pair Correlations Between Fermions -- 17.7. Uncertainty Relations for a Many-Fermion System -- 17.8. Pair Correlation Function for Noninteracting Bosons -- 17.9. Bogoliubov Transformation for a Many-Boson System
17.10. Scattering of Two Quasi-Particles -- 17.11. Bogoliubov Transformation for Fermions Interacting through Pairing Forces -- 17.12. Damped Harmonic Oscillator -- 18.1. Coherent State of the Radiation Field -- 18.2. Casimir Force -- 18.3. Casimir Force Between Parallel Conductors -- 18.4. Casimir Force in a Cavity with Conducting Walls -- 19.1. Theory of Natural Line Width -- 19.2. The Lamb Shift -- 19.3. Heisenberg's Equations for Interaction of an Atom with Radiation -- 20.1. EPR Experiment with Particles -- 20.2. Classical and Quantum Mechanical Operational Concepts of Measurement -- 20.3. Collapse of the Wave Function -- 20.4. Quantum versus Classical Correlations
Summary This book provides a detailed account of quantum theory with a much greater emphasis on the Heisenberg equations of motion and the matrix method
The book features a deeper treatment of the fundamental concepts such as the rules of constructing quantum mechanical operators and the classical-quantal correspondence; the exact and approximate methods based on the Heisenberg equations; the determinantal approach to the scattering theory and the LSZ reduction formalism where the latter method is used to obtain the transition matrix. The uncertainty relations for a number of different observables are derived and discussed. A comprehensive chapter on the quantization of systems with nonlocalized interaction is included. Exact solvable models, and approximate techniques for solution of realistic many-body problems are also considered. The book takes a unified look in the final chapter, examining the question of measurement in quantum theory, with an introduction to the Bell's inequalities. --Book Jacket
Bibliography Includes bibliographical references and index
Notes English
Print version record
Subject Quantum theory.
SCIENCE -- Physics -- Quantum Theory.
Quantum theory
Form Electronic book
ISBN 9789814304122
9814304123
9781283148399
1283148390
9786613148391
6613148393