Quantum Physics I

This lecture covers the fundamental concepts of quantum physics, including vector spaces, commutators, observables, and the Heisenberg uncertainty principle. The instructor explains the implications of observables commuting or not commuting, leading to the concept of diagonalization. The lecture delves into the Stone theorem, unitary operators, and the Schrödinger equation. The discussion includes the time evolution of quantum states, the Hamiltonian operator, energy eigenvalues, and the importance of diagonalizing the Hamiltonian. The lecture concludes with a detailed explanation of how to solve the Schrödinger equation and interpret the results in terms of energy eigenstates and their time evolution.