3890ps11_10 - Chem 3890 Physical Chemistry I Fall 2010...

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Unformatted text preview: Chem 3890 Physical Chemistry I Fall 2010 Chemistry 3890 Problem Set 11 Fall 2010 A grade it yourself problem set. Solutions will be posted after the last week of class. Last revised: November 28, 2010 Approximations are the most precious fruits of theory. V. Ostrovsky Problem 1 Define two single particle states a ( x ) = bracketleftBig bracketrightBig 1 / 4 e- ( x- x ) 2 / 2 (1a) b ( x ) = bracketleftBig bracketrightBig 1 / 4 e- ( x + x ) 2 / 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, ) ( b | a ) = 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...
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3890ps11_10 - Chem 3890 Physical Chemistry I Fall 2010...

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