Quantum Mechanics I
Physics 5370 Syllabus

[After J.J. Sakurai, “Modern Quantum Mechanics”, Chs.1-4.]

Fundamental Concepts

• The Stern-Gerlach experiment
• Kets, bras and operators
• Base kets and matrix representations
• Measurements, observables and uncertainty relations
• Change of basis
• Position, momentum and translation
• Wave functions in position and momentum space

Quantum Dynamics

• Time Evolution and the Schrodinger equation
• The Schrodinger versus the Heisenberg picture
• Simple Harmonic Oscillator
• Schrodinger’s wave equation
• Propagators and Feynman path integrals
• Potentials and gauge transformations
• Magnetic monopoles

Theory of Angular Momentum

• Rotations and angular momentum commutation relations
• Spin 1/2 systems and finite rotations
• O(3), SU(2) and Euler rotations
• Density operators and pure versus mixed ensembles
• Eigenvalues and eigenstates of angular momentum
• Orbital angular momentum
• Addition of angular momenta
• Tensor operators

Symmetry in Quantum Mechanics

• Symmetries, conservation laws and degeneracies
• Discrete symmetries, parity, or space inversion
• Lattice translation as a discrete symmetry
• The time-reversal discrete symmetry