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 - Gram-Schmidt 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 Gram-Schmidt 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