Linear Algebra and Quantum Mechanics

Quantum mechanics is a fascinating theory that lies at the heart of our understanding of nature at small scales. It uses some of the most beautiful and clear mathematical concepts: vector spaces and complex numbers. These concepts might seem abstract, but when applied to the real world, they lead to exciting physical phenomena such as wave–particle duality or Heisenberg's famous uncertainty principle! Thus, our primary goal would be to learn the essential mathematical tools used in quantum mechanics: vector spaces, matrices, eigenvectors, commutators, and complex numbers. Once we grasp these tools, we will use them to study another fascinating physical concept: the spin of an elementary particle!