1. Historical Motivation
2. Postulates of Quantum Mechanics
3. Wave Functions and the Schrodinger Equation
4. Operators and Observables
5. One-Dimensional Problems
6. Angular Momentum and the Hydrogen Atom
7. Spin
8. Approximation Methods
9. Problem Set
10. Identical Particles and Exchange Symmetry
11. Variational Methods
12. Time-Dependent Perturbation Theory
13. Scattering Theory
14. WKB Approximation
15. Density Functional Theory: Conceptual Overview

University-level quantum mechanics notes covering postulates, operators, and approximation methods.

• Postulates: State vectors, observables, measurement, time evolution
• Wave Functions: Schrodinger equation, probability interpretation, normalisation
• Operators: Commutation relations, uncertainty principle, eigenvalues
• Approximation Methods: Perturbation theory, variational method, WKB

• Classical mechanics (Lagrangian, Hamiltonian)
• Linear algebra (vector spaces, operators, eigenvalues)
• Differential equations (ordinary and partial)
• Complex numbers and Fourier transforms

Start with the historical motivation to understand the context, then progress to postulates and operators. Each section includes worked examples and practice problems.

Use the sidebar to browse topics, or start with the introductory pages linked from the sidebar.

Each section includes:

• Detailed explanations of key concepts
• Worked examples with step-by-step solutions
• Practice problems with answers
• Common pitfalls and how to avoid them
• Connections to other areas of physics

1. Master the postulates: Understand the physical meaning of each postulate
2. Practise problems: Work through many problems to build intuition
3. Draw diagrams: Visualise wave functions and probability distributions
4. Learn symmetries: Understand conservation laws and selection rules
5. Connect to applications: Relate quantum mechanics to atomic, molecular, and particle physics