Introduction to quantum Mechanics

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. Introduction. Brief history of Quantum Physics. Complex numbers. Theory of probabilities.
2. Vector spaces with complex coefficients. "bra" and "ket" notation. Probability theory.
3. Postulates of Quantum Mechanics.
4. Spin. Pauli matrices.
5. ummary of classical mechanics. Hamiltonian function and Poisson brackets.
6. Schrödinger equation. Quantum harmonic oscillator.
7. Combination of two spins.
8. Entangled states.

Bibliography

• Villate, J. E. (2025). 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).