Unformatted text preview: Chemistry 550 / 475 – Homework Assignment #4 due: Friday, October 21st at 5:00 pm Readings : Chapters 4 and 5 in Levine Problem 1  GramSchmidt orthogonalization. Let  φ 1 ) ≡  1 ) and  φ 2 ) ≡  2 ) represent two linearly independent states (kets) that are not orthogonal nor are they normalized to unity. a. Show that one can always find a linear combination of them orthogonal to  1 ) . b. Extending the results in part a. , show that given N linearly independent kets  k ) , k = 1 ,...,N, one can always find N mutually orthogonal linear combinations of these kets. This general procedure is basically the GramSchmidt orthogonalization process. Problem 2  Simultaneous measurement. A pair of linear Hermitian operators A and B commute if and only if they share a common complete set of eigenfunctions. Prove this statement. Problem 3  Measurement of an evolving quantum state [550 only]. Problem 7.37 in Levine....
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This note was uploaded on 01/18/2012 for the course CHEM 550/475 taught by Professor Davidj.masiello during the Fall '11 term at University of Washington.
 Fall '11
 DavidJ.Masiello
 Chemistry

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