Introduction to quantum Mechanics

Objective

To explain the fundamental concepts of Quantum Mechanics. After attending this course you should be able to explain the postulates of quantum mechanics, solve simple problems in that area, and understand basic concepts such as particle-wave duality, uncertainty principle, exclusion principle and quantum entanglement.

Program

1. Introduction. Summary of analytical mechanics. Complex numbers. Theory of probabilities.
2. Brief history of Quantum Physics. Light. Atomic structure.
3. Vector spaces with complex coefficients. "bra" and "ket" notation.
4. Postulates of Quantum Mechanics. Heisenberg picture.
5. Spin. Pauli matrices.
6. Combination of two spins. External product of vector spaces.
7. Entangled states.

Bibliography

• Villate, J. E. (2026). Introdução à Mecânica Quântica (in Portuguese). Author's edition, Porto.
• Susskind, L. & Friedman, A. (2014). Quantum Mechanics. The Theoretical Minimum.
• Zubairy, M. S. (2020). Quantum Mechanics for Beginners, with applications to quantum communication and quantum computing.
• 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

• Apontamentos (in Portuguese).
• Interference of light.
• História das teorias da Luz (in Portuguese).
• Exhibition of Experiments about Light.
• Introdução à computação quântica (in Portuguese).