16_580ln_fa08

16_580ln_fa08 - MIT OpenCourseWare http/ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these

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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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Fall, 2008 Page 1 of 6 pages Lecture #16: Parity and e/f Basis for 2 , 2 ± Last Time: H = H ROT + H SO + H SS + H SR for 2 , 2 * two identical blocks for 2 > 0 and < 0 * 2 ~ 2 matrix elements involve L ± and cannot be evaluated explicitly. Define: β = B n L + n ′∑ v v v v A L + n ′∑ α = n v v v v 2 Caution: we do not know relationship between two similar appearing symbols. ? E.g. n Λ = + 1L + n ′Λ = 0 = n Λ = 1L n ′Λ = 0 . Another caution: The 2 block of the matrix does not factor into > 0 and < 0 sub- blocks. 2 + 1/2 E − γ 2 + B v y 2 sym v 2 B ) y E γ 2 + B y 2 2 1/2 ( γ v v v y = J + 1/2 = 2 + 1/2 H 2 1/2 2 + 1/2 B v ( J S + ) + γ + 1 J S + 2 1/2 2 = ( γ 2 B ) [ J(J + y 1) (1/ 2)( 1/ 2) ] 1/2 [ S(S + 1) 1 (1/ 2)( 1/ 2) ] 1/2 v So are we wrong about being able to factor H into two identical blocks? Not quite. Today: Parity σ ˆ ( xz ) v HLB-RWF pages 74-75, 138-145 * apply σ ˆ v to 3 parts of | and to operators JTH, pages 15-22, 23-25 * mysterious phases for α , β matrix elements * ± parity and e/f basis functions Derive full 2 , 2 + , 2 e f Effective Hamiltonian expressed in terms of E, B, A, γ , α , β What happens when we apply σ ˆ v ( xz ) [reflection in body frame] to | v ? Trivial. What happens when we apply
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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16_580ln_fa08 - MIT OpenCourseWare http/ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these

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