** **

**Stern-Gerlach experiments:** The quantum state vector

**Rotation of basis states:** Beginnings of matrix mechanics**,** rotation operators**,** identity and projection operators**,** matrix representation of operators**,** changing representations**,** expectation values

**Angular momentum:** Commuting operators**,** eigenvalues and eigenstates**,** raising and lowering operators**,** uncertainty relations

**Time evolution:** The Hamiltonian and the Schroedinger equation**,** time dependence of expectation values**,** precession of spin ½ in a magnetic field**,** magnetic resonance**,** energy-time uncertainty relation

**System of spin ½ particles:** Basis states for two spin ½ particles**,** hyperfine splitting**,** addition of angular momenta for two spin ½ particles, EPR paradox, Bell inequalities

**Wave mechanics in 1D:** Position eigenstates and the wave function**,** translation operator**,** generator of translations**,** momentum operator in the position basis**,** momentum space, Gaussian wave packet, Heisenberg uncertainty principle, particle in a box, scattering in one dimension

**1D harmonic oscillator:** Operator methods**,** raising and lowering operators**,** position space wave functions**,** zero point energy**,** classical limit**,** time dependence

**Wave mechanics in 3D:** Translational invariance and conservation of linear momentum**,** rotational invariance and conservation of angular momentum**,** a complete set of commuting observables**,** position space representation of the angular momentum operator**,** orbital angular momentum eigenfunctions, Coulomb potential**,** infinite spherical well

**Organization**

Lectures M W F 10:00 - 10:50 AM

Homework (30%) Weekly problem sets

Term exam (30%)

Final exam (40%)

Text: John S. Townsend, *A modern approach to quantum mechanics*

*All information is representative only, and is likely to change from year to year.*