More details provided in the syllabus.

Assignments

1. due Tuesday, September 9
2. due Thursday, September 18
3. (ungraded) preparation for the test on Thursday, September 25
4. due Tuesday, October 14
5. due Tuesday, October 28
6. due Tuesday, November 18

Lectures

1. Review of the syllabus; differences between classical and quantum mechanics in the Lagrangian and Hamiltonian schemes; features of QM that break our classical intuition; Dirac notation and the operator formalism; linear vector spaces; orthonormality and completeness of states; time evolution of quantum states; expectation values and matrix elements; position representation; wave function of a freely propagating particle—see Robinett 1.1–1.5, 6.1–6.2, 12.1–12.2; Fitzpatrick 3.1–3.4
2. Probabilistic interpretation of QM; position and momentum representations as Fourier transform pairs; momentum operator; particle in a nonzero potential; properties of the wave function; current operator and continuity equation for the local probability density—see Robinett 3.1–3.2, 4.1–4.5; Fitzpatrick 2.1–2.5, 3.14–3.16
3. Probabilty current arising from a spatially varying phase angle; time evolution of expectation values; commutator relations; stationary states; eigenfunctions and eigenvalues; inner products and the expansion postulate—see Robinett 4.6–4.8, 12.4–12.5; Fitzpatrick 4.1–4.12
4. Expansion in a complete basis of energy eigenstates; closure relation; normalization; expectation value of energy; measurement postulate; infinite square well; continuity and smoothness of the wave function; reflection symmetry and the parity of the wave function—see Robinett 5.1–5.3, 6.3–6.7; Fitzpatrick 5.1–5.2
5. Finite square well; applying matching conditions for a piecewise-defined wave function; particle in a double well; two-level systems—see Robinett 8.2; Fitzpatrick 5.7
6. Review of Assignment 1; image potential near a metallic surface—see Robinett 8.3; Fitzpatrick 7.1–7.3
7. Exponential envelope in the asymptotic limit; power series solutions; barrier tunnelling problems; transmission and reflection coefficients—see Robinett 11.1–11.2; Fitzpatrick 5.8, 9.4, 5.3
8. Transfer Matrix approach to barrier tunnelling
9. Bras, kets, and the relationship to linear algebra; matrix mechanics using a finite basis set; review of Assignment 3—see Robinett Ch 10.4
10. Review of the first in-class test; expansion postulate; basis of free-particle states and the relationship to Fourier transforms—see Robinett 2.2–2.3
11. Time evolution of a wavefunction in a basis of energy eigenstates—see Fitzpatrick 4.9, 4.11–12
12. Gaussian wave packets; probability current; dispersion; tunnelling—see Robinett Ch 2.5; Fitzpatrick 3.10–3.13
13. Expectation values and their time dependence; numerical approaches based on discretization and iteration; cutoffs and resolution; spectral methods—see Robinett 10.1, Fitzpatrick 3.15, 4.1–4.5
14. Quantum harmonic oscillator (QHO), factorization and second quantization—see Robinett 9.1–9.2, 13.1–13.3; Fitzpatrick 5.8
15. QHO, manipulation of ladder operators, Hermite polynomials, vibrational modes of diatomic molecules—see Robinett E.3, 9.3
16. Two-dimensional QHO—see Robinett 15.1
17. Formalism for two interacting particles in three-dimensional space, hydrogen atom, transformation to centre-of-mass and relative coordinates, separability, components of angular momentum and their operator algebra—see Robinett 14.1–14.3, 16.1; Fitzpatrick 6.4
18. Spherical coordinates, angular momentum eigenstates, vibrational and rotational modes of diatomic molecules—see Robinett 16.2–16.3; Fitzpatrick 8.1–8.7