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Transcript
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 (t) d ih (t) H(t)(t) dt 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 (t 0 ) Postulates of Quantum Mechanics (from “quantum mechanics” by Claude Cohen-Tannoudji) 2nd postulate: Every measurable physical quantity is described by an operator Qˆ . Q This operator is an observable. 3rd postulate: The only possible result of the measurement of a physical quantity Q is one of the eigenvalues of the corresponding observable Qˆ . 4th postulate (non-degenerate): When the physical quantity Q is measured on a system in the normalized state the probability of ˆ is obtaining the eigenvalue an of the corresponding observable Q P an un 2 where un is the normalizedeigenvector of associated with the eigenvalue an . Qˆ Physical interpretation of 2 * is a probability density. The probability of finding the particle in the volume element 2 x, y,z,t dxdydz. General solution for x, y,z,t Try separation of variables: dxdydz at time n t e iEn t / h and is x, y,z,t n x, y,z n t Plug into TDSE to arrive at the pair of linked equations: t Hˆ n E nn Orthogonality: For a , b which are different eigenvectors of we have orthogonality: * ab 0 bra/ket Let us prove this to introduce the notation used in the textbook Hn E nn
