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CITATION

McMahon, David. Quantum Mechanics Demystified. McGraw-Hill Professional, 2005.

Quantum Mechanics Demystified

Authors: David McMahon

Published:  November 2005

eISBN: 9780071486705 0071486704 | ISBN: 9780071455466
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  • Contents
  • Preface
  • Acknowledgments
  • Chapter 1 Historical Review
  • Blackbody Radiation and Planck’s Formula
  • The Photoelectric Effect
  • The Bohr Theory of the Atom
  • de Broglie’s Hypothesis
  • Quiz
  • Chapter 2 Basic Developments
  • The Schrödinger Equation
  • Solving the Schrödinger Equation
  • The Probability Interpretation and Normalization
  • Expansion of the Wavefunction and Finding Coefficients
  • The Phase of a Wavefunction
  • Operators in Quantum Mechanics
  • Momentum and the Uncertainty Principle
  • The Conservation of Probability
  • Quiz
  • Chapter 3 The Time Independent Schrödinger Equation
  • The Free Particle
  • Bound States and 1-D Scattering
  • Parity
  • Ehrenfest Theorem
  • Quiz
  • Chapter 4 An Introduction to State Space
  • Basic Definitions
  • Hilbert Space Definitions
  • Quiz
  • Chapter 5 The Mathematical Structure of Quantum Mechanics I
  • Linear Vector Spaces
  • Basis Vectors
  • Expanding a Vector in Terms of a Basis
  • Orthonormal Sets and the Gram-Schmidt Procedure
  • Dirac Algebra with Bras and Kets
  • Finding the Expansion Coefficients in the Representation of Bras and Kets
  • Quiz
  • Chapter 6 The Mathematical Structure of Quantum Mechanics II
  • The Representation of an Operator
  • Eigenvalues and Eigenvectors
  • The Hermitian Conjugate of an Operator
  • The Commutator
  • Quiz
  • Chapter 7 The Mathematical Structure of Quantum Mechanics III
  • Change of Basis and Unitary Transformations
  • The Generalized Uncertainty Relation
  • Projection Operators
  • Functions of Operators
  • Generalization to Continuous Spaces
  • Quiz
  • Chapter 8 The Foundations of Quantum Mechanics
  • The Postulates of Quantum Mechanics
  • Spectral Decomposition
  • Projective Measurements
  • The Completeness Relation
  • Completely Specifying a State with a CSCO
  • The Heisenberg versus Schrödinger Pictures
  • Describing Composite Systems in Quantum Mechanics
  • The Matrix Representation of a Tensor Product
  • The Tensor Product of State Vectors
  • The Density Operator
  • The Density Operator for a Completely Mixed State
  • A Brief Introduction to the Bloch Vector
  • Quiz
  • Chapter 9 The Harmonic Oscillator
  • The Solution of the Harmonic Oscillator in the Position Representation
  • The Operator Method for the Harmonic Oscillator
  • Number States of the Harmonic Oscillator
  • More on the Action of the Raising and Lowering Operators
  • Quiz
  • Chapter 10 Angular Momentum
  • The Commutation Relations of Angular Momentum
  • The Uncertainty Relations for Angular Momentum
  • Generalized Angular Momentum and the Ladder Operators
  • Matrix Representations of Angular Momentum
  • Coordinate Representation of Orbital Angular Momentum and the Spherical Harmonics
  • Quiz
  • Chapter 11 Spin-1/2 Systems
  • The Stern-Gerlach Experiment
  • The Basis States for Spin-1/2 Systems
  • Using the Ladder Operators to Construct S[sub(x)], S[sub(y)]
  • Unitary Transformations for Spin-1/2 Systems
  • The Outer Product Representation of the Spin Operators
  • The Pauli Matrices
  • The Time Evolution of Spin-1/2 States
  • The Density Operator for Spin-1/2 Systems
  • Quiz
  • Chapter 12 Quantum Mechanics in Three Dimensions
  • The 2-D Square Well
  • An Overview of a Particle in a Central Potential
  • An Overview of the Hydrogen Atom
  • Quiz
  • Final Exam
  • Answers to Quiz and Exam Questions
  • References
  • Index