Postulates of Quantum Mechanics (from “quantum mechanics” by Claude Cohen-Tannoudji) 6th postulate: The time evolution of the state vector is governed by the Schroedinger equation where H(t) is the observable associated with the total energy of the system. 1st postulate: At a fixed time t0, the state of a physical system is defined by specifying a ket

Postulates of Quantum Mechanics (from “quantum mechanics” by Claude Cohen-Tannoudji) 2nd postulate: Every measurable physical quantity is described by an operator This operator is an observable. 3rd postulate: The only possible result of the measurement of a physical quantity is one of the eigenvalues of the corresponding observable 4th postulate (non-degenerate): When the physical quantity is measured on a system in the normalized state the probability of obtaining the eigenvalue of the corresponding observable is where is the normalized eigenvector of associated with the eigenvalue

Physical interpretation of is a probability density. The probability of finding the particle in the volume element at time is General solution for Try separation of variables: Plug into TDSE to arrive at the pair of linked equations: and

Orthogonality: For which are different eigenvectors of we have orthogonality: Let us prove this to introduce the bra/ket notation used in the textbook