ECE615_Lecture_20

ECE615_Lecture_20 - (1 where full permutation operator...

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Unformatted text preview: (1) where- full permutation operator, defined such that the expression that follow it is to be summed over all permutations of the frequencies , that is, over all put and output frequencies. The Cartesian indices are to be permuted along with the Lecture 20 ( 29( 29 ( 29 (3) 3 ( ; , , ) P k j i h gn nm ml l g kjih r q p F lmn ng mg q p l g p N σ σ μ μ μ μ χ ϖ ϖ ϖ ϖ ε ϖ ϖ ϖ ϖ ϖ ϖ ϖ =---- ∑ ℏ Quantum Mechanical Model of Nonresonant Electronic Nonlinearities: r q p σ ϖ ϖ ϖ ϖ = + + P F , , , and r q p σ ϖ ϖ ϖ ϖ input and output frequencies. The Cartesian indices are to be permuted along with the frequencies. The final result is then to be divided by the number of permutations of the input frequencies. In the low frequency limit 1 4 2 2 2 2 3 ( ) 4 / 32 me Rydberg ea a me Bohr ϖ μ π ε π ε = = - =- ℏ ℏ 4 2 (3) 22 3 3 2 m : ~ ~ 10 V N QM μ χ ε ϖ- ℏ 4 (3) 3 6 2 : ~ Ne AnharOscillator m d χ ε ϖ Become the same if we use: Organic liquids that are composed of anisotropic molecules (anisotropic polarizability...
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ECE615_Lecture_20 - (1 where full permutation operator...

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