We emphasize that this distinction between the state of a quantum system (given by the wave function) and the observables, which we can extract from it, is the novelty of quantum mechanics with respect to classical physics where this notion is absent. Now, we need to introduce a concept and a mathematical language required to extract information about the physical properties of a system from its state vector, which we will denote by observables. We also discussed their matrix representation and how we can express a state vector in terms of its components in a specific basis. We presented the Dirac notation and discussed that we can assign a probabilistic interpretation to vector states and their inner products. We saw that the state of a quantum system is described by its vector state, an element of a special complex vector space called the Hilbert space. In the previous lecture, we presented the mathematical language to describe the quantum states of a physical system. The total length of the videos: ~5 minutes The action of an operator on kets in matrix representation The contents of this lecture are supplemented with the following videos:Ģ.
Definition and properties of operatorsĪnd at the end of the lecture notes, there is a set the corresponding exercises: The lecture on operators in quantum mechanics consists of the following parts:ĥ.1.
