Quantum mechanics I
Undergraduate · Physics
Syllabus focus
Standard syllabus · Theoretical / proof-based
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Topics typically covered
Standard syllabus
Foundations and one dimension
- Wave–particle duality and the Schrödinger equation
- Probability density and normalization
- Infinite square well and finite barriers
- Tunneling and transmission coefficients
- Harmonic oscillator (algebraic and series methods)
Formalism and three dimensions
- Hilbert space, bras and kets, and operators
- Commutators and uncertainty principle
- Separation of variables in 3D
- Hydrogen atom: quantum numbers and spectra
- Spin-½ and Stern–Gerlach experiment
Approximation methods
- Time-independent perturbation theory
- Degenerate perturbation and fine structure (intro)
- Variational principle for ground states
- WKB approximation (overview)
- Identical particles and Pauli exclusion preview
Theoretical / proof-based
Operator algebra
- Self-adjoint operators and observable spectra
- Completeness of eigenfunctions in separable systems
- Projection operators and measurement postulates
- Ehrenfest theorem and classical correspondence
- Angular momentum algebra and Clebsch–Gordan (intro)
Symmetry and representations
- Conservation laws from commutators
- Parity and time-reversal symmetry
- Rotation group SO(3) and spinor representations
- Addition of angular momentum
- Landau levels as symmetry example (optional)
Mathematical foundations
- Delta-function potentials and boundary conditions
- Spectral theorem intuition for QM
- Hermitian vs unitary time evolution
- Path integral motivation (Feynman sketch)
- Density matrices and mixed states (intro)
Notes
Topics reflect common upper-division physics syllabi at US colleges and universities. Prerequisites, lab pairing, and mathematical depth vary by department.