Phys402, II-Semester 2016/17, Quiz 6, solution

Instructor: Sebastian Wuster

part (1): The following sketches show the harmonic oscillator approximation of twomolecular electronic states s = 0, 1. Indices ν label the vibrational states. Upon dipoleexcitation from s = 0, ν = 0 to s′ = 1, use the Frank Condon principle to infer whichvibrational state ν ′ is most likely excited on the upper surface, among those shown, forthe cases A-C.

s=0

s’=1

01234

01234

A B C

ν

ν’

R R R

E

A: ν ′=4 has the largest overlapp with ν = 0, by visual inspection.B: ν ′=0, the potentials are unshifted, so all other ν ′ are orthogonal to ν = 0.C: ν ′=1, by careful visual inspection.

part (2): For the following molecular transitions, state which one are allowed bydipole-selection rules in the harmonic approximation:

(i) | sνKmK 〉 = | 0030 〉 → | s′ν ′K ′m′K 〉 = | 0041 〉 yes

(ii) | sνKmK 〉 = | 0030 〉 → | s′ν ′K ′m′K 〉 = | 1330 〉 yes, electronic transition can

have any ∆ν, see part (1)

(iii) | sνKmK 〉 = | 0030 〉 → | s′ν ′K ′m′K 〉 = | 0321 〉 no, non-electronic transition can

have only |∆ν| = 1 in the harmonic approximation.

(iv) | sνKmK 〉 = | 0432 〉 → | s′ν ′K ′m′K 〉 = | 5622 〉 yes

1