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9: Review of the basic postulates of quantum mechanics

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    • 9.1: Measurement
      The result of a measurement of the observable A must yield one of the eigenvalues of A^ . Thus, we see why A is required to be a hermitian operator: Hermitian operators have real eigenvalues.
    • 9.2: Physical Observables
    • 9.3: The Fundamental Postulates of Quantum Mechanics
    • 9.4: The Heisenberg Picture
      In all of the above, notice that we have formulated the postulates of quantum mechanics such that the state vector evolves in time, but the operators corresponding to observables are taken to be stationary. This formulation of quantum mechanics is known as the Schrödinger picture. However, there is another, completely equivalent, picture in which the state vector remains stationary and the operators evolve in time. This picture is known as the Heisenberg picture.
    • 9.5: The Heisenberg Uncertainty Principle
      Because the operators x and p are not compatible, [X,P]≠0, there is no measurement that can precisely determine both x and p simultaneously. Hence, there must be an uncertainty relation between them that specifies how uncertain we are about one quantity given a definite precision in the measurement of the other. Presumably, if one can be determined with infinite precision, then there will be an infinite uncertainty in the other.
    • 9.6: The Physical State of a Quantum System
      The physical state of a quantum system is represented by a vector denoted |Ψ(t)⟩ which is a column vector, whose components are probability amplitudes for different states in which the system might be found if a measurement were made on it.
    • 9.7: Time Evolution of the State Vector
      The time evolution of the state vector is prescribed by the Schrödinger equation.

    This page titled 9: Review of the basic postulates of quantum mechanics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Mark Tuckerman.

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