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Unformatted text preview: Chemistry 550 / 475 – Homework Assignment #2 due: Friday, October 7th at 5:00 pm Readings : Chapters 1 - 3 in Levine Problem 1 - Quantum number of a macroscopic system. Problem 2.10 in Levine. Problem 2 - Commutators. Evaluate the commutators of the following operators: a. [ x, p x ] and [ x, p 2 x ] b. [ x, p z ] and [ x, p 2 z ] c. [ x , p ] and [ x , p 2 ] d. [ x, V ( x )] and [ x , V ( x )] e. [ x , H ] = [ x , p 2 / 2 m + V ( x )] and [ p , H ] = [ p , p 2 / 2 m + V ( x )] Recall that x = x ˆ e x + y ˆ e y + z ˆ e z and p = p x ˆ e x + p y ˆ e y + p z ˆ e z in three-dimensional Cartesian coordinates. Problem 3 - Units. What are the units of the normalized Schr¨ odinger wave function describing one particle in one dimension? How about one particle in three dimensions? And two particles in three dimensions? You may want to consider the following integrals integraldisplay ∞-∞ Ψ * ( x )Ψ( x ) dx = 1 and integraldisplay V Ψ * ( x 1 , x 2 , ··· , x N )Ψ( x 1 , x 2 , ··· , x N ) d 3 x = 1 involving the normalized wave functions Ψ....
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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