hw4 - Chemistry 550 475 – Homework Assignment#4 due...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Ask a homework question - tutors are online