TY  - BOOK
AU  - Shankar,Ramamurti
TI  - Principles of quantum mechanics
SN  - 9788181286864
AV  - QC174.12 .S52 1994
U1  - 530.1/2 20
PY  - 1994///
CY  - New York
PB  - Springer
KW  - Quantum theory
N1  - 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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