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Heisenberg's quantum mechanics /

This book provides a detailed account of quantum theory with a much greater emphasis on the Heisenberg equations of motion and the matrix method.

Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Razavy, Mohsen
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Singapore ; Hackensack, N.J. : World Scientific, ©2011.
Temas:	Quantum theory. Théorie quantique. SCIENCE > Physics > Quantum Theory.
Acceso en línea:	Texto completo

Tabla de Contenidos:

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.

Heisenberg's quantum mechanics /

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