Principles of Quantum Mechanics – R. Shankar – 1st Edition

Descripción

El objetivo de este libro es proporcionarle una introducción a la , a partir de sus axiomas. El objetivo de este capítulo es equiparlo con la matemática necesaria. Toda la matemática que necesitará se desarrolla aquí, a partir de algunas ideas básicas sobre vectores y que se supone que conoce. Se dan numerosos ejemplos y ejercicios relacionados con la mecánica clásica, tanto para aliviar un poco las como para demostrar la amplia aplicabilidad de las ideas desarrolladas aquí. El esfuerzo que ponga en este capítulo valdrá la pena: no solo lo preparará para este curso, sino que también unificará muchas ideas que puede haber aprendido poco a poco. Para aprender realmente este capítulo, debe, como con cualquier otro capítulo, resolver los problemas

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  • 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)
    3.5. Conclusions
    4. The Postulates—a General Discussion
    4.1. The Postulates
    4.2. Discussion of Postulates I–III
    4.3. The Schrödinger Equation (Dotting Your i’s and Crossing your ?’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 Schrödinger Equation
    8.6. Potentials of the Form V = a + bx + cx2 + d? + ex?
    9. The Heisenberg Uncertainty Relations
    9.1. Introduction
    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. Translational Invariance in Quantum Theory
    11.2. Time Translational Invariance
    11.3. Parity Invariance
    11.4. 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 Lz
    12.4. Angular Momentum in Three Dimensions
    12.5. The Eigenvalue Problem of L
    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
    14.1. Introduction
    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
    19.1. Introduction
    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
    Appendix
    A.1. Matrix Inversion
    A.2. Gaussian Integrals
    A.3. Complex Numbers
    A.4. The i? Prescription
    ANSWERS TO SELECTED EXERCISES
  • Citar Libro
    • Título: Principles of Quantum Mechanics
    • Autor/es:
    • ISBN-10: 0306447908
    • Edición: 1ra Edición
    • Año de edición: 2013
    • Tema: Física
    • Subtema: Mecánica Cuántica
    • Tipo de Archivo: Libro
    • Idioma: eBook en Inglés

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