Sample lecture schedule
(based on 25 lectures each
of duration 75 minutes).
- Lecture 1:
Review
of undergrad QM, part 1: Hilbert space, states and observables,
measurement, uncertainty relation, identical particles, two-state
system.
- Lecture 2:
Review
of undergrad QM, part 2: Schrödinger
equation, harmonic oscillator, angular momentum, “ideal”
hydrogen atom.
- Lecture 3:
Time-independent
perturbation theory.
- Lecture 4:
The
“real” hydrogen atom.
- Lecture 5:
Identical
particles, exchange interaction, helium atom.
- Lecture 6:
Many-body
states, Slater determinant, Hartree-Fock approximation.
- Lecture 7:
Variational
method: hydrogen molecule, chemical binding.
- Lecture 8:
Periodic
potential, Bloch waves, band structure.
- Lecture 9:
Time-dependent
perturbation theory, Fermi’s Golden Rule.
- Lecture 10:
Application
to two-state system (e.g., spin rotations, NMR).
- Lecture 11:
Elementary
two-state systems: neutral kaons or neutrino oscillations.
- Lecture 12:
Continuous
symmetries, Noether’s theorem, rotation group SO(3).
- Lecture 13:
Addition
of angular momenta 1.
- Lecture 14:
Addition
of angular momenta, Clebsch-Gordon coefficients.
- Lecture 15:
Tensor
operators, Wigner-Eckart theorem.
- Lecture 16:
SU(2)
and its relationship to SO(3), isospin (weak & strong).
- Lecture 17:
Path
integral formulation of QM: Principles, free particle.
- Lecture 18:
Path
integral – semiclassical limit.
- Lecture 19:
WKB
approximation.
- Lecture 20:
Path
integral – example: particle on a circle, Berry’s phase.
- Lecture 21:
Scattering
theory: cross section, S-matrix, T-matrix, unitarity.
- Lecture 22:
Scattering
theory: Born approximation.
- Lecture 23:
Scattering
theory: Partial waves, optical theorem.
- Lecture 24:
Special
topics.
- Lecture 25:
Special
topics.
Choice of
special topics: quantum information theory, renormalization group,
etc.
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