Introduction to quantum Mechanics

Any student at the University of Porto can enroll in this course.

Objective

To provide the minimum knowledge necessary to understand the fundamental concepts of Quantum Mechanics. After attending this course you should be able to explain the postulates of quantum mechanics, solve Schrödinger's equation in simple cases and understand basic quantum mechanics concepts such as particle-wave duality, uncertainty principle, exclusion principle and quantum entanglement.

Program

1. Mathematical background. Vector spaces on the complex field. "bra" and "ket" notation. Probability theory.
2. Particles and waves. Linear momentum. Kinetic and potential energy. Angular momentum. Wave motion. Waves interference. Diffraction.
3. History. Theories of light. Balck-body radiation. Atomic models.
4. Quantum mechanics foundations. Energy quantization. Particle-wave duality. Probabilistic interpretation. Uncertainty principle.
5. Quantum model of the electron. De Broglie waves. Bose-Einstein condensation. Electrons dispersion.
6. Quantum model of light. Photons. Polarization. Malus law. Beam splitters.
7. Superposition and quantum entanglement. Coherent superposition of states. Entanglement and Bell's bases. Schrödinger's cat paradox. Quantum teleportation. quantum cloning.
8. Schrödinger equation. Solution of the one-dimensional Schrödinger: particle inside a box. Tunneling. Solution of the Schrödinger equation in three dimensions: hydrogen atom.

Bibliography

• Zubairy, M. S. (2020). Quantum Mechanics for Beginners, with applications to quantum communication and quantum computing.
• Susskind, L. & Friedman, A. (2014). Quantum Mechanics. The Theoretical Minimum.
• Feynman R. P., Leighton, R. B & Sands, M. (1965). The Feynman Lectures on Physics, Volume III.
• Jordan, T. F. (1986). Quantum mechanics in simple matrix form.
• van Dommelen, L. (2011). Quantum Mechanics for Engineers.
• Institute for Quantum Computing, University of Waterloo (2024). What is quantum mechanics?

Support Material

• Interference of light.
• História das teorias da Luz (in Portuguese).
• Experiments about Light. Exhibition.