Quantum Mechanics

Notes on the formal structure of non-relativistic quantum mechanics.

Contents

1. Mathematical Preliminaries — Hilbert spaces, bra–ket notation, operators, eigenstates, observables, tensor products, density operators.
2. Postulates of Quantum Mechanics — the seven standard postulates: state space, observables, Born rule, measurement collapse, Schrödinger evolution, composite systems, symmetrization.
3. The Heisenberg Picture — equivalent reformulation in which operators carry the time dependence and states are fixed; comparison with Schrödinger and interaction pictures.
4. Path Integral Formulation — Feynman's sum-over-paths formulation, including preliminaries on Lagrangian mechanics, functionals, Wick rotation, and the generating functional.