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Postulates of Quantum Mechanics

Postulates of Quantum Mechanics. (from “quantum mechanics” by Claude Cohen-Tannoudji). 6 th 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.

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Postulates of Quantum Mechanics

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  1. 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

  2. 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

  3. 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

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

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