Assume that the electronic states of the re electrons of a conjugated molecule can be approximated by the wave functions of a particle in a one-dimensional box, and that the dipole moment can be related to the displacement along this length by μ= -ex. Show that the transition probability for the transition n = 1 → 7 n = 2 is nonzero, whereas that for n = 1 →7 n = 3 is zero. Hint. The following relations will be useful:

Transcribed Image Text:

sin x sin y cos(x-y)-1 cos(x + y) x cos ax dx =-cos ax +--sin ax