3890ps6_09 - Chem 3890 Physical Chemistry I Fall 2009...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Chem 3890 Physical Chemistry I Fall 2009 Chemistry 3890 Problem Set 6 Fall 2009 Due: in class, Friday, October 23 Last revised: October 19, 2009 Additions/corrections: Problem 1 The Hermite polynomials H n [ ] (Griffith, Sec. 2.3, see also http://mathworld.wolfram.com/ HermitePolynomial.html ) satisfy the following relations ( n a non-negative integer) H prime n = 2 nH n- 1 (1a) H n +1 = 2 H n- 2 nH n- 1 (1b) where H prime d H n / d . 1. Using these relations, show that Hermites equation is satisfied: H primeprime n- 2 H prime n + 2 nH n = 0 . (2) Normalized HO eigenstates are (McQ&S, 5.6) n ( x ) = bracketleftbigg 2 n n ! bracketrightbigg 1 2 H n ( x ) e- x 2 / 2 , n = 0 , 1 , 2 , . . . (3) where m/ planckover2pi1 . 2. Use the above information to derive expressions for the matrix elements ( n prime | x | n ) integraldisplay + - d x * n prime ( x ) x n ( x ) (4a) and ( n prime | p | n ) integraldisplay + - d x * n prime ( x ) p n ( x ) (4b) for general n and n prime (non-negative integers) . 3. Evaluate the expectation values ( x ) n ( n | x | n ) , ( x 2 ) n , ( p ) n , and ( p 2 ) n ....
View Full Document

Page1 / 3

3890ps6_09 - Chem 3890 Physical Chemistry I Fall 2009...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online