QM2 · Formalism
A 24-module path through qm2 · formalism, in study order from foundations to the frontier.
Modules
- Hilbert Space and State Vectors
- Dirac Bra-Ket Notation
- Inner Product and Norm of States
- Linear Operators on Hilbert Space
- Hermitian Operators and Observables
- Eigenvalues and Eigenstates
- Complete Orthonormal Bases
- Completeness Relation and Resolution of Identity
- Projection Operators
- The Postulates of Quantum Mechanics
- Born Rule and Measurement Probabilities
- Measurement and Wavefunction Collapse
- Expectation Values and Variance
- The Commutator and Compatible Observables
- Simultaneous Diagonalization and Complete Sets of Commuting Observables
- Generalized Uncertainty Principle
- Position Representation
- Momentum Representation
- Canonical Commutation Relation
- Continuous Spectra and Dirac Delta Normalization
- Density Operator and Mixed States
- Hermitian Conjugate and Adjoint Operators
- Unitary Operators and Transformations
- Rigged Hilbert Space