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Unformatted text preview: Chem 3890 Physical Chemistry I Fall 2009 Chemistry 3890 Problem Set 10 Fall 2009 Due: in class, Friday, December 4 Last revised: November 28, 2009 Approximations are the most precious fruits of theory. V. Ostrovsky Problem 1 Define two single particle states a ( x ) = bracketleftbigg 2 bracketrightbigg 1 / 4 e- ( x- x ) 2 (1a) b ( x ) = bracketleftbigg 2 bracketrightbigg 1 / 4 e- ( x + x ) 2 (1b) where- x + , > 0, x 0. These are normalized Gaussian wavepackets centered at x = x , respectively. Note : unless otherwise indicated, perform the following calculations for general real ( > 0) and x ( 0). 1. Calculate the overlap between states a and b , S ( x, ) integraldisplay + - d x * b ( x ) a ( x ) . (2) Plot S versus x for 0 x 2 (set = 1). 2. Define the 2-particle quantum state for distinguishable particles 1 and 2: ( x 1 ,x 2 ) = a ( x 1 ) b ( x 2 ) . (3) Is normalized?...
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