Shankar, Ramamurti.
Principles of quantum mechanics / R. Shankar. - 2nd ed. - New York : Plenum Press, c1994. - xviii, 676 p. : ill. ; 27 cm.
Includes bibliographical references and index.
Mathematical Introduction -- Linear Vector Spaces: Basics -- Inner Product Spaces -- Dual Spaces and the Dirac Notation -- Subspaces -- Linear Operators -- Matrix Elements of Linear Operators -- Active and Passive Transformations -- The Eigenvalue Problem -- Functions of Operators and Related Concepts -- Generalization to Infinite Dimensions -- Review of Classical Mechanics -- The Principle of Least Action and Lagrangian Mechanics -- The Electromagnetic Lagrangian -- The Two-Body Problem -- How Smart Is a Particle? -- The Hamiltonian Formalism -- The Electromagnetic Force in the Hamiltonian Scheme -- Cyclic Coordinates, Poisson Brackets, and Canonical Transformations -- Symmetries and Their Consequences -- All Is Not Well with Classical Mechanics -- Particles and Waves in Classical Physics -- An Experiment with Waves and Particles (Classical) -- The Double-Slit Experiment with Light -- Matter Waves (de Broglie Waves) -- The Postulates - a General Discussion -- The Postulates -- Discussion of Postulates I-III -- The Schrodinger Equation (Dotting Your i's and Crossing your h's) -- Simple Problems in One Dimension -- The Free Particle -- The Particle in a Box -- The Continuity Equation for Probability -- The Single-Step Potential: a Problem in Scattering -- The Double-Slit Experiment -- Some Theorems -- The Classical Limit -- The Harmonic Oscillator -- Why Study the Harmonic Oscillator? -- Review of the Classical Oscillator -- Quantization of the Oscillator (Coordinate Basis) -- The Oscillator in the Energy Basis -- Passage from the Energy Basis to the X Basis -- The Path Integral Formulation of Quantum Theory -- The Path Integral Recipe -- Analysis of the Recipe -- An Approximation to U(t) for the Free Particle -- Path Integral Evaluation of the Free-Particle Propagator -- Equivalence to the Schrodinger Equation -- Potentials of the Form V = a + bx + cx[superscript 2] + dx + exx -- The Heisenberg Uncertainty Relations -- Derivation of the Uncertainty Relations -- The Minimum Uncertainty Packet -- Applications of the Uncertainty Principle -- The Energy-Time Uncertainty Relation -- Systems with N Degrees of Freedom -- N Particles in One Dimension -- More Particles in More Dimensions -- Identical Particles -- Symmetries and Their Consequences -- Overview -- Translational Invariance in Quantum Theory -- Time Translational Invariance -- Parity Invariance -- Time-Reversal Symmetry -- Rotational Invariance and Angular Momentum -- Translations in Two Dimensions -- Rotations in Two Dimensions -- The Eigenvalue Problem of L[subscript z] -- Angular Momentum in Three Dimensions -- The Eigenvalue Problem of L[superscript 2] and L[subscript z] -- Solution of Rotationally Invariant Problems -- The Hydrogen Atom -- The Eigenvalue Problem -- The Degeneracy of the Hydrogen Spectrum -- Numerical Estimates and Comparison with Experiment -- Multielectron Atoms and the Periodic Table -- Spin -- What is the Nature of Spin? -- Kinematics of Spin -- Spin Dynamics -- Return of Orbital Degrees of Freedom -- Addition of Angular Momenta -- A Simple Example -- The General Problem -- Irreducible Tensor Operators -- Explanation of Some "Accidental" Degeneracies -- Variational and WKB Methods -- The Variational Method -- The Wentzel-Kramers-Brillouin Method -- Time-Independent Perturbation Theory -- The Formalism -- Some Examples -- Degenerate Perturbation Theory -- Time-Dependent Perturbation Theory -- The Problem -- First-Order Perturbation Theory -- Higher Orders in Perturbation Theory -- A General Discussion of Electromagnetic Interactions -- Interaction of Atoms with Electromagnetic Radiation -- Scattering Theory -- Recapitulation of One-Dimensional Scattering and Overview -- The Born Approximation (Time-Dependent Description) -- Born Again (The Time-Independent Approximation) -- The Partial Wave Expansion -- Two-Particle Scattering -- The Dirac Equation -- The Free-Particle Dirac Equation -- Electromagnetic Interaction of the Dirac Particle -- More on Relativistic Quantum Mechanics -- Path Integrals - II -- Derivation of the Path Integral -- Imaginary Time Formalism -- Spin and Fermion Path Integrals. Summary -- App. A.1. Matrix Inversion -- App. A.2. Gaussian Integrals -- App. A.3. Complex Numbers -- App. A.4. The i[epsilon] Prescription. 1. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1.10. 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 3. 3.1. 3.2. 3.3. 3.4. 4. 4.1. 4.2. 4.3. 5. 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 6. 7. 7.1. 7.2. 7.3. 7.4. 7.5. 8. 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 9. 9.2. 9.3. 9.4. 9.5. 10. 10.1. 10.2. 10.3. 11. 11.1. 11.2. 11.3. 11.4. 11.5. 12. 12.1. 12.2. 12.3. 12.4. 12.5. 12.6. 13. 13.1. 13.2. 13.3. 13.4. 14. 14.2. 14.3. 14.4. 14.5. 15. 15.1. 15.2. 15.3. 15.4. 16. 16.1. 16.2. 17. 17.1. 17.2. 17.3. 18. 18.1. 18.2. 18.3. 18.4. 18.5. 19. 19.2. 19.3. 19.4. 19.5. 19.6. 20. 20.1. 20.2. 20.3. 21. 21.1. 21.2. 21.3. 21.4.
0306447908
94026837
Quantum theory.
QC174.12 / .S52 1994
530.12 / SHP
Principles of quantum mechanics / R. Shankar. - 2nd ed. - New York : Plenum Press, c1994. - xviii, 676 p. : ill. ; 27 cm.
Includes bibliographical references and index.
Mathematical Introduction -- Linear Vector Spaces: Basics -- Inner Product Spaces -- Dual Spaces and the Dirac Notation -- Subspaces -- Linear Operators -- Matrix Elements of Linear Operators -- Active and Passive Transformations -- The Eigenvalue Problem -- Functions of Operators and Related Concepts -- Generalization to Infinite Dimensions -- Review of Classical Mechanics -- The Principle of Least Action and Lagrangian Mechanics -- The Electromagnetic Lagrangian -- The Two-Body Problem -- How Smart Is a Particle? -- The Hamiltonian Formalism -- The Electromagnetic Force in the Hamiltonian Scheme -- Cyclic Coordinates, Poisson Brackets, and Canonical Transformations -- Symmetries and Their Consequences -- All Is Not Well with Classical Mechanics -- Particles and Waves in Classical Physics -- An Experiment with Waves and Particles (Classical) -- The Double-Slit Experiment with Light -- Matter Waves (de Broglie Waves) -- The Postulates - a General Discussion -- The Postulates -- Discussion of Postulates I-III -- The Schrodinger Equation (Dotting Your i's and Crossing your h's) -- Simple Problems in One Dimension -- The Free Particle -- The Particle in a Box -- The Continuity Equation for Probability -- The Single-Step Potential: a Problem in Scattering -- The Double-Slit Experiment -- Some Theorems -- The Classical Limit -- The Harmonic Oscillator -- Why Study the Harmonic Oscillator? -- Review of the Classical Oscillator -- Quantization of the Oscillator (Coordinate Basis) -- The Oscillator in the Energy Basis -- Passage from the Energy Basis to the X Basis -- The Path Integral Formulation of Quantum Theory -- The Path Integral Recipe -- Analysis of the Recipe -- An Approximation to U(t) for the Free Particle -- Path Integral Evaluation of the Free-Particle Propagator -- Equivalence to the Schrodinger Equation -- Potentials of the Form V = a + bx + cx[superscript 2] + dx + exx -- The Heisenberg Uncertainty Relations -- Derivation of the Uncertainty Relations -- The Minimum Uncertainty Packet -- Applications of the Uncertainty Principle -- The Energy-Time Uncertainty Relation -- Systems with N Degrees of Freedom -- N Particles in One Dimension -- More Particles in More Dimensions -- Identical Particles -- Symmetries and Their Consequences -- Overview -- Translational Invariance in Quantum Theory -- Time Translational Invariance -- Parity Invariance -- Time-Reversal Symmetry -- Rotational Invariance and Angular Momentum -- Translations in Two Dimensions -- Rotations in Two Dimensions -- The Eigenvalue Problem of L[subscript z] -- Angular Momentum in Three Dimensions -- The Eigenvalue Problem of L[superscript 2] and L[subscript z] -- Solution of Rotationally Invariant Problems -- The Hydrogen Atom -- The Eigenvalue Problem -- The Degeneracy of the Hydrogen Spectrum -- Numerical Estimates and Comparison with Experiment -- Multielectron Atoms and the Periodic Table -- Spin -- What is the Nature of Spin? -- Kinematics of Spin -- Spin Dynamics -- Return of Orbital Degrees of Freedom -- Addition of Angular Momenta -- A Simple Example -- The General Problem -- Irreducible Tensor Operators -- Explanation of Some "Accidental" Degeneracies -- Variational and WKB Methods -- The Variational Method -- The Wentzel-Kramers-Brillouin Method -- Time-Independent Perturbation Theory -- The Formalism -- Some Examples -- Degenerate Perturbation Theory -- Time-Dependent Perturbation Theory -- The Problem -- First-Order Perturbation Theory -- Higher Orders in Perturbation Theory -- A General Discussion of Electromagnetic Interactions -- Interaction of Atoms with Electromagnetic Radiation -- Scattering Theory -- Recapitulation of One-Dimensional Scattering and Overview -- The Born Approximation (Time-Dependent Description) -- Born Again (The Time-Independent Approximation) -- The Partial Wave Expansion -- Two-Particle Scattering -- The Dirac Equation -- The Free-Particle Dirac Equation -- Electromagnetic Interaction of the Dirac Particle -- More on Relativistic Quantum Mechanics -- Path Integrals - II -- Derivation of the Path Integral -- Imaginary Time Formalism -- Spin and Fermion Path Integrals. Summary -- App. A.1. Matrix Inversion -- App. A.2. Gaussian Integrals -- App. A.3. Complex Numbers -- App. A.4. The i[epsilon] Prescription. 1. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1.10. 2. 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 3. 3.1. 3.2. 3.3. 3.4. 4. 4.1. 4.2. 4.3. 5. 5.1. 5.2. 5.3. 5.4. 5.5. 5.6. 6. 7. 7.1. 7.2. 7.3. 7.4. 7.5. 8. 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 9. 9.2. 9.3. 9.4. 9.5. 10. 10.1. 10.2. 10.3. 11. 11.1. 11.2. 11.3. 11.4. 11.5. 12. 12.1. 12.2. 12.3. 12.4. 12.5. 12.6. 13. 13.1. 13.2. 13.3. 13.4. 14. 14.2. 14.3. 14.4. 14.5. 15. 15.1. 15.2. 15.3. 15.4. 16. 16.1. 16.2. 17. 17.1. 17.2. 17.3. 18. 18.1. 18.2. 18.3. 18.4. 18.5. 19. 19.2. 19.3. 19.4. 19.5. 19.6. 20. 20.1. 20.2. 20.3. 21. 21.1. 21.2. 21.3. 21.4.
0306447908
94026837
Quantum theory.
QC174.12 / .S52 1994
530.12 / SHP