MIT5_74s09_lec04_3

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MIT OpenCourseWare http://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Andrei Tokmakoff, MIT Department of Chemistry, 5/19/2005 4-16 4.3. EINSTEIN B COEFFICIENT AND ABSORPTION CROSS-SECTION The rate of absorption induced by the field is 2 2 w k A () ω = π 2 ˆ k ε μ A δ ( k A ) (4.56) E 0 2 = The rate is clearly dependent on the strength of the field. The variable that you can most easily measure is the intensity I , the energy flux through a unit area, which is the time-averaged value of the Poynting vector, S S = c ( E B ) × (4.57) 4 c E 2 = c E 0 2 . (4.58) I = S = 4 8 (Note, I’ve rather abruptly switched units to cgs). Using this we can write 2 ˆ w = I k εμ A δω , (4.59) ( k A ) k A 3 4 c = 2 2 where I have also made use of the uniform distribution of polarizations applicable to an isotropic 1 2 field: Ex ˆ ⋅= Ey ˆ = Ez ˆ = . An equivalent representation of the amplitude of a 0 0 0 E 0 3
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MIT5_74s09_lec04_3 - MIT OpenCourseWare http/ocw.mit.edu...

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