Quantum Physics I

This lecture covers the fundamental postulates of quantum physics, including the state vector postulate and the measurement postulate. The instructor explains how physical properties are represented by state vectors and how measurements collapse the state into eigenstates of the observable. The lecture delves into the concept of compatible and incompatible observables, showcasing examples with spin measurements. The importance of commutators in determining compatibility is highlighted, leading to a discussion on the uncertainty principle. The transformation of operators between different bases using unitary operators is also explored, emphasizing the preservation of inner products. The lecture concludes with a practical exercise on changing bases and representing operators in different bases.