Contents -- Preface -- 1 A Brief Survey of Analytical Dynamics -- 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 Inflnitesimal 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 -- Bibliography -- 2 Discovery of Matrix Mechanics -- 2.1 Equivalence of Wave and Matrix Mechanics -- Bibliography -- 3 Mathematical Preliminaries -- 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 -- 3.11 Summation Over Normal Modes -- Bibliography -- 4 Postulates of Quantum Theory -- 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 -- Bibliography -- 5 Equations of Motion, Hamiltonian Operator and the Commutation Relations -- 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 -- Bibliography -- 6 Symmetries and Conservation Laws -- 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 -- Bibliography -- 7 Bound State Energies for One-Dimensional Problems -- 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 -- Bibliography -- 8 Exactly Solvable Potentials, Supersymmetry and Shape Invariance -- 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 -- Bibliography -- 9 The Two-Body Problem -- 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 -- 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 for Angular Momentum -- 9.13 Generalized Spin Operators -- 9.14 The Ladder Operator -- Bibliography.

10 Methods of Integration of Heisenberg's Equations of Motion -- 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 -- Bibliography -- 11 Perturbation Theory -- 11.1 Perturbation Theory Applied to the Problem of a Quartic Oscillator -- 11.2 Degenerate Perturbation Theory -- 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 -- Bibliography -- 12 Other Methods of Approximation -- 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 -- Bibliography -- 13 Quantization of the Classical Equations of Motion with Higher Derivatives -- 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 -- Bibliography -- 14 Potential Scattering.

14.1 Determinantal Method in Potential Scattering -- 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 -- Bibliography -- 15 Quantum Diffraction -- 15.1 Diffraction in Time -- 15.2 High Energy Scattering from an Absorptive Target -- Bibliography -- 16 Motion of a Charged Particle in Electromagnetic Field and Topological Quantum Effects for Neutral Particles -- 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 -- Bibliography -- 17 Quantum Many-Body Problem -- 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 -- Bibliography -- 18 Quantum Theory of Free Electromagnetic Field -- 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 -- Bibliography -- 19 Interaction of Radiation with Matter -- 19.1 Theory of Natural Line Width -- 19.2 The Lamb Shift -- 19.3 Heisenberg's Equations for Interaction of an Atom with Radiation -- Bibliography -- 20 Bell's Inequality -- 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 -- Bibliography -- Index.