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Functions and operators:Bilinear expansion of linear operators, Hermitian operators

<< The time-dependent Schrödinger equation:Quantum mechanical measurement and expectation values
Operators and quantum mechanics:Commutation of operators, General form of the uncertainty principle >>



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Table of Contents:
  1. Introduction:Quantum mechanics and real life, Quantum mechanics as an intellectual achievement
  2. Waves and quantum mechanics – Schrödinger’s equation:Diffraction by two slits
  3. The time-dependent Schrödinger equation:Quantum mechanical measurement and expectation values
  4. Functions and operators:Bilinear expansion of linear operators, Hermitian operators
  5. Operators and quantum mechanics:Commutation of operators, General form of the uncertainty principle
  6. Approximation methods in quantum mechanics:Degenerate perturbation theory, Variational method
  7. Time-dependent perturbation theory:Simple oscillating perturbations, Refractive index
  8. Quantum mechanics in crystalline materials:One electron approximation, Band structure
  9. Angular momentum:L squared operator, Visualization of angular momentum
  10. The hydrogen atom:Multiple particle wavefunctions, Coordinates for the hydrogen atom problem
  11. Methods for one-dimensional problems:Transfer matrix, Electron emission with a potential barrier
  12. Spin:Angular momentum and magnetic moments, Direct product spaces and wavefunctions with spin
  13. Identical particles:Pauli exclusion principle, Extension to more than two identical particles
  14. The density matrix:Pure and mixed states, Time-evolution of the density matrix
  15. Harmonic oscillators and photons:Quantization of electromagnetic fields, Field operators
  16. Fermion operators:Postulation of fermion annihilation and creation operators, Wavefunction operator
  17. Interaction of different kinds of particles:Operators for systems with different kinds of particles
  18. Quantum information:Quantum mechanical measurements and wavefunction collapse, Quantum computing
  19. Interpretation of quantum mechanics:Hidden variables and Bell’s inequalities, Epilogue
  20. Appendix A Background mathematics:Exponential and logarithm notation
  21. Appendix B Background physics:Elementary classical mechanics, Waves and diffraction
  22. Appendix C Vector calculus:Spherical polar coordinates, Cylindrical coordinates
  23. Appendix D Maxwell’s equations and electromagnetism:Maxwell’s equations in free space
  24. Appendix E Perturbing Hamiltonian for optical absorption:Quantum mechanical Hamiltonian
  25. Appendix F Early history of quantum mechanics
  26. Appendix G Some useful mathematical formulae:Formulae for sines, cosines, and exponentials
  27. Appendix H Greek alphabet
  28. Appendix I Fundamental constants
  29. Bibliography
  30. Memorization list
  31. Index