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Principles of quantum mechanics /

by Shankar, Ramamurti.

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BookPublisher: New York : Plenum Press, c1994Edition: 2nd ed.Description: xviii, 676 p. : ill. ; 27 cm.ISBN: 0306447908.Subject(s): Quantum theory

Contents:

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.

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Item type	Current location	Collection	Call number	Copy number	Status	Date due	Barcode
Books	Dhaka University Science Library General Stacks	Non Fiction	530.12 SHP (Browse shelf)	1	Available		393997
Books	Dhaka University Science Library General Stacks	Non Fiction	530.12 SHP (Browse shelf)	2	Available		393998

Includes bibliographical references and index.

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

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Principles of quantum mechanics /

by Shankar, Ramamurti.