Lect8_DensityOperator - Lecture 8: The Density Operator The...

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Lecture 8: The Density Operator The goal of quantum mechanics is to make predictions regarding the outcomes of measurements Using the formalism we have developed so far, the procedure is as follows: Take an initial state vector Evolve it according to Schrödinger's equation until the time the measurement takes place Use the projector onto eigenstates of the observable to predict the probabilities for different results To confirm the prediction, one would prepare a system in a known initial state, make the measurement, then re-prepare the same initial state and make the same measurement after the same evolution time. With enough repetitions, the results should show statistical agreement with the results of quantum theory Expectation Value The expectation value of an operator is defined (with respect to state | ! " ) as: The interpretation is the average of the results of many measurements of the observable A on a system prepared in state | " . Proof:
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.

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Lect8_DensityOperator - Lecture 8: The Density Operator The...

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