Here are some notes and examples that I’ve written while following through the edX online course MIT 8.05x (Mastering Quantum Mechanics). Please note that I won’t be posting solutions to any of the homework problems from that course.

**Chapter 1 – Wave mechanics**

**Chapter 3 – Linear Algebra I**

- 3.01 Vector spaces: definitions and examples

- 3.02 Subspaces and direct sums
- 3.02 Vector spaces: span, linear independence and basis
- 3.03 Linear operators & commutators
- 3.04 Linear operators: null space, range, injectivity and surjectivity
- 3.04 Inverses of linear operators
- 3.05 Matrix representation of linear operators; matrix multiplication
- 3.05 Matrix representation of linear operators: change of basis
- 3.06 Eigenvalues and eigenvectors

**Chapter 4 – Linear Algebra II**

- 4.01 Inner products and Hilbert spaces
- 4.02 Orthonormal basis and orthogonal complement
- 4.02 Projection operators
- 4.03 Linear functionals and adjoint operators
- 4.04 Hermitian operators – a few more theorems
- 4.04 Unitary operators

**Chapter 5 – Dirac’s bra and ket notation**

**Chapter 6 – Uncertainty principle and compatible operators**