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MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY ± Chemistry 5.76± Spring 1977± Problem Set #1 Due February 14, 1977 1. Carry out the angular momentum algebra indicated in Section 2 (of Steinfeld, Chapter 1); that is, show explicitly that 11 z | j x | 11 z = 0, and that J 2 x − � J x 2 0. 2. (a) Given the matrix elements of the coordinate x for a harmonic oscillator: v | x | v = ψ v x ψ v dx = 0 unless v = v ± 1 and v + 1 | x | v = (2 β ) 1 / 2 ( v + 1) 1 / 2 v 1 | x | v = (2 β ) 1 / 2 ( v ) 1 / 2 where β = 4 π 2 m ω/ h , and ω is the vibrational frequency. ± Evaluate the non-zero matrix elements of x 2 , x 3 , and x 4 ; that is, evaluate the integrals± v | x r | v = ψ v x r ψ v dx for r = 2 , 3 , and 4 (without
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