Time evolution of a quantum system

Professor Susskind opens the lecture by presenting the four fundamental principles of quantum mechanics that he touched on briefly in the last lecture.  He then discusses the evolution in time of a quantum system, and describes how the classical concept of reversibility relates to the quantum mechanical principle of conservation of information, which is actually the conservation of distinctions or distinguishability of states.  The evolution in time of a quantum system is represented by unitary operators which preserve distinctions and overlap.

Professor Susskind then derives the time-dependent Schrödinger equation, and describes how to calculate the expected value of an observable, and how it changes with time.  This discussion introduces the commutator operator.  Professor Susskind closes the lecture by showing the connection between the quantum mechanical commutator and the Poisson bracket formulation of classical physics, thus showing how the time evolution of the expected value of an observable is closely related to classical equations of motion.