Quantum Mechanics Lecture Notes
OPTI 570, Fall semester 2020
Prof. Brian P. Anderson
College of Optical Sciences
University of Arizona
Contents
Section 1. - Wavefunction spaces, State spaces, Dirac notation
Section 2. - Representations in state space
Section 3. - Eigenvalue equations, observables
Section 4. - Unitary operators
Section 5. - {Ir>} and {Ip>} representations, R & P operators
Section 6. - Postulates of Quantum Mechanics
Section 7. - Evolution, Shrodinger & Heisenberg pictures, stationary states
Section 8. - Free-particle wavepackets - example problem
Section 9. - Quantum harmonic oscillator
Section 10. - Energy eigenstates of the harmonic oscillator
Section 11. - Harmonic oscillator: properties of the energy eigenstates
Section 12. - Angular momentum in quantum mechanics
Section 13. - Spin 1/2
Section 14. - Two-level systems
Section 15. - Density operator
Section 16. - Unitary operators and rotations (rotations not covered in class)
Section 17. - Using rotation operators: j > 1/2 (not covered in class)
Section 18. - Angular momentum and rotations (not covered in class)
Section 19. - The hydrogen atom
Section 20. - Tensor products
Section 21. - Addition of angular momentum
Section 22. - Stationary perturbation theory
Section 23. - (removed)
Section 24. - Fine and hyperfine structure of hydrogen
Section 25. - Zeeman effect
Section 26. - Time-dependent perturbation theory
Section 27. - Optical Physics example problem
Appendix B - Summary of topics, second half of semester
Appendix FT - Fourier transforms in perturbation theory
Appendix RF - Time-dependent reference frames
Appendix OP - revised version of optical physics example problem of sec. 27
