Nonrelativistic Quantum Mechanics

The following sections are included:

• Preface to the First and Second Editions

• Preface to the Third Edition

• Contents

The following sections are included:

• Introduction

• Blackbody Radiation

• Stability of Atoms: Discrete Spectral Lines

• Photoelectric Effect

• Wave Particle Duality
  • Reflection
  • Refraction

• de Broglie's Hypothesis

• The Compton Effect

• The Davisson-Germer Experiment

• The Franck-Hertz Effect

• Planck's Radiation Law

• Einstein's Model for Specific Heat

• The Debye Model

• Bohr Model and the Hydrogen Atom

• Problems

• Bibliography

The following sections are included:

• Introduction

• Classical Mechanics: Particle in One Dimension

• Lagrangian and Hamiltonian Formulation

• Contact Transformations: Hamilton-Jacobi Theory

• Interpretation of Action-Angle Variables

• Hydrogen Atom: Bohr-Sommerfeld Quantization

• The Schrödinger Equation

• Problems

• Bibliography

The following sections are included:

• Introduction

• Plane Wave Solutions

• Conservation Law for Particles

• Young's Double Slit Experiment

• The Superposition Principle and Group Velocity

• Formal Considerations

• Ambiguities
  • Use of Different Coordinate Systems
  • Non-Commutativity

• Interaction with an Electromagnetic Field

• Problems

• Bibliography

The following sections are included:

• Introduction

• Particle in a Box

• Parity

• Scattering from a Step-Function Potential
  • Boundary Conditions
  • Particles from the Left
  • Interpretation of R and S

• Finite Square Well: Bound States

• Tunneling Through a Square Barrier
  • Resonance Transmission

• Time Reversal

• Problems

• Bibliography

The following sections are included:

• Introduction

• General Considerations

• The Simple Harmonic Oscillator
  • Generating Function for Hermite Polynomials
  • Rodrigues Formula for Hermite Polynomials
  • Normalization

• The Delta Function

• Attractive Delta Function Potential

• Repulsive Delta Function Potential

• Square Well: Scattering and Phase Shifts

• Periodic Potentials
  • Floquet's Theorem
  • Bloch's Theorem

• The Kronig-Penney Problem

• Problems

• Bibliography

The following sections are included:

• Introduction

• Geometry of Hilbert Space

• ℒ₂: A Model Hilbert Space

• Operators on Hilbert Space: Mainly Definitions

• Cayley Transform: Self-Adjoint Operators

• Some Properties of Self-Adjoint Operators

• Classification of Symmetric Operators

• Spontaneously Broken Symmetry

• Problems

• Bibliography

The following sections are included:

• Introduction

• Al - Physical States

• A2 - Observables

• A3 - Probabilities

• A4 - Reduction of the Wave Packet
  • Example

• Compatibility Theorem and Uncertainty Principle

• The Heisenberg Microscope

• A5 - The Schrödinger Equation

• Time Evolution: Constants of the Motion

• Time-Energy Uncertainty Relation

• Time Evolution of Probability Amplitudes

• Problems

• Bibliography

The following sections are included:

• Introduction

• Functionals

• Fourier Transforms

• Rigged Hilbert Spaces

• Problems

• Bibliography

The following sections are included:

• Introduction

• Simple Harmonic Oscillator
  • Expectation Values

• The Rigid Rotator

• 3D Rigid Rotator: Angular Momentum

• Algebraic Approach to Angular Momentum

• Rotations and Rotational Invariance

• Spin Angular Momentum

• Problems

• Bibliography

The following sections are included:

• Introduction

• The Radial Equation

• Infinite Square Well

• Simple Harmonic Oscillator: Cartesian Coordinates
  • Degeneracy

• Simple Harmonic Oscillator: Spherical Coordinates

• The Hydrogenic Atom
  • Laguerre Polynomials

• Reduction of the Two-Body Problem

• Problems

• Bibliography

The following sections are included:

• Introduction

• Rotations in a Vector Space
  • Fourier Transform of Hermite Functions

• Dirac Notation

• Coherent States
  • The Forced Simple Harmonic Oscillator

• Quasi-classical States

• Squeezed States

• Example: Angular Momentum

• Schrödinger Picture

• Heisenberg Picture

• Dirac or Interaction Picture

• Hidden Variables

• Problems

• Bibliography

The following sections are included:

• Introduction

• Rayleigh-Schrödinger Perturbation Theory

• First Order Perturbations

• Anharmonic Oscillator

• Ground State of Helium-like Ions

• Second Order Perturbations

• Displaced Simple Harmonic Oscillator

• Non-degenerate Perturbations to all Orders

• Sum Rule: Second Order Perturbation

• Linear Stark Effect

• Problems

• Bibliography

The following sections are included:

• Introduction

• Two Levels: Rayleigh-Schrödinger Method

• Rayleigh-Schrödinger: Degenerate Levels

• Example: Spin Hamiltonian
  • Exact Solution
  • Rayleigh-Schrödinger Solution

• Problems

• Bibliography

The following sections are included:

• Introduction

• Rayleigh-Ritz Method

• Example: Simple Harmonic Oscillator

• Example: He Ground State

• The WKB Approximation
  • Turning points

• WKB Applied to a Potential Well
  • Special Boundaries

• WKB Approximation for Tunneling

• Alpha Decay
  • Heuristic Discussion
  • Detailed Analysis

• Problems

• Bibliography

The following sections are included:

• Introduction

• Formal Considerations

• Transition Amplitudes

• Time-Independent Perturbation

• Periodic Perturbation of Finite Duration

• Photo-Ionization of Hydrogen Atom

• The Adiabatic Approximation

• The Sudden Approximation

• Dipole in a Time-Dependent Magnetic Field
  • Oscillatory Perturbation
  • Slowly Varying Perturbation
  • Sudden Approximation

• Two-Level Systems

• Berry's Phase

• Problems

• Bibliography

The following sections are included:

• Introduction

• Gauge Transformations

• Motion in a Uniform Magnetic Field
  • Classical Hall Effect
  • Landau Levels

• Crossed Electric and Magnetic Fields
  • The Quantum Hall Effect

• Magnetic Field: Heisenberg Equations

• Energy Eigenfunctions

• Translation Invariant States

• Gauge Transformations

• Problems

• Bibliography

The following sections are included:

• Introduction

• Spin and Spin-Orbit Coupling

• Alkali Spectra

• Addition of Angular Momenta

• Two Spin ½ States

• Spin ½ + Orbital Angular Momentum

• The Weak-Field Zeeman Effect

• The Aharonov-Bohm Effect

• Problems

• Bibliography

The following sections are included:

• Introduction

• Classical Scattering Theory

• Asymptotic States: Schrödinger Picture

• The Møller Wave Operators

• Green's Functions and Propagators

• Integral Equations for Propagators

• Cross-Sections

• The Lippmann-Schwinger Equations

• The S-Matrix and the Scattering Amplitude

• Problems

• Bibliography

The following sections are included:

• Introduction

• The Scattering Amplitude

• Green's Functions

• The Born Approximation

• The Yukawa Potential

• Free Particle in Spherical Coordinates

• Partial Wave Analysis

• Phase Shifts

• The Optical Theorem: Unitarity Bound

• Partial Waves: Lippmann-Schwinger Equation

• Effective Range Approximation

• Resonant Scattering

• Problems

• Bibliography

The following sections are included:

• Introduction

• Two Identical Particles

• The Hydrogen Molecule

• N Identical Particles

• Non-Interacting Fermions

• Non-Interacting Bosons

• N-Space: Second Quantization for Bosons

• N-Space: Second Quantization for Fermions

• Field Operators in the Schrödinger Picture

• Representation of Operators

• Heisenberg Picture

• Problems

• Bibliography

The following sections are included:

• Introduction

• The Density Matrix
  • The Microcanonical Ensemble
  • The Canonical Ensemble
  • The Grand Canonical Ensemble

• The Ideal Gases

• General Properties of the Density Matrix

• The Density Matrix and Polarization

• Composite Systems

• von Neumann's Theory of Measurement

• Decoherence

• Conclusion

• Problems

• Bibliography

The following sections are included:

• Index