Quantum Physics I

This lecture focuses exclusively on discrete degrees of freedom, studying observables described by operators and their associated physics. It delves into examples like spin and harmonic molecules, introducing the Dirac notation to extend the theory to continuous degrees of freedom. The lecture explores the formalism of position and momentum operators, Poisson brackets, and the correspondence between classical and quantum mechanics, emphasizing the importance of symmetries and canonical commutation relations. The discussion also covers the concept of Hamiltonian dynamics, the Schrödinger equation, and the role of operators in quantum dynamics.