... ðA1:8Þ ðA1:9Þ Outline of Density Matrix Analysis 287 transforms the equation of motion into that in the interaction picture: ½HI ðtÞ, I ðtÞ i h HI ðtÞ ¼ U0 ðtÞy HI ðtÞU0 ðtÞ d=dtI ðtÞ ¼ ðA1 :10 aÞ ... ðtÞ d=dtI ðtÞ ¼ ðA1 :10 aÞ ðA1 :10 bÞ where HI(t) is the interaction Hamiltonian in the interaction picture Let h En ¼ !n be the energy eigenvalues of jni; then the density matrix elements Inn0 ... interaction picture, the expectation value of A is given by È É hAi ¼ Tr I ðtÞAI ðtÞ , AI ðtÞ ¼ U0 ðtÞy AU0 ðtÞ Copyright © 2004 Marcel Dekker, Inc ðA1 :11 Þ ðA1 :12 Þ ...