Permutation operators in quantum mechanics

How does the permutation of particles work in quantum mechanics? 📚 In this video we learn about permutation operators, which allow us to exchange particles in quantum mechanics. We start with a simple example using balls and boxes to introduce the idea of a permutation, which amounts to a re-ordering of the balls, and the idea of a transposition, which amounts to an exchange of two balls. We then see how these ideas can be used to define permutation operators --the tool that allows us to exchange quantum particles--, and we also have a brief taster of group theory. Projection operators are essential for the mathematical study of systems of identical particles, for example the electrons in atoms, molecules, or materials. 🐦 Follow me on Twitter: https://twitter.com/ProfMScience ⏮️ BACKGROUND Tensor product state spaces: https://youtu.be/kz3206S2B6Q Operators in quantum mechanics: https://youtu.be/pNFna7zZbgE Adjoint operators: https://youtu.be/b_DcsVCtP5I Hermitian operators: https://youtu.be/XIgDUfyrLAY ⏭️ WHAT NEXT? Symmetric and antisymmetric states: https://youtu.be/6pwtOV5mUpo Exchange degeneracy: https://youtu.be/-HMZNk6VlZ0 The symmetrization postulate: https://youtu.be/hOY51y9iqGQ ~ Director and writer: BM Producer and designer: MC