hint - alternatively, work it out by considering the...

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Chemistry 550 / 475 – Homework Assignment #5 (HINTS) due: Friday, October 28th at 5:00 pm Readings : Chapters 4 and 5 in Levine Problem 1 - Eigenfunctions of the harmonic oscillator. There are many useful relations involving Hermite polynomials. In addition to H n ( z ) = ( - ) n e z 2 ( d n /dz n ) e - z 2 you may also find the following facts useful: 1 2 n n ! π Z -∞ H n ( z ) H m ( z ) e - z 2 dz = δ nm zH n ( z ) = nH n - 1 ( z ) + 1 2 H n +1 ( z ) Based upon this information you will be able to solve h n | m i , h n | x | m i , and h n | x 2 | m i in terms of oscillator eigenfunctions. However, evaluating h n | x k | m i is more complicated. You may either use your knowledge of parity to state, in words, when this integral is nonzero, or,
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Unformatted text preview: alternatively, work it out by considering the following relation X n,p,k =0 I nkp s n n ! t k k ! (2 ) p p ! = e 2 +2( st + s + t ) , where I nkp is the following useful integral I nkp = Z - H n ( z ) H k ( z ) e-z 2 z p dz for n,k,p nonnegative integers. This latter sum may be used to compute I nkp by comparing equal powers of s n t k p ....
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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.

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