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Uniform WKB Wavefunctions and Franck-Condon Factors
Uniform WKB Wavefunctions and Franck-Condon Factors
Journal of the Korean Chemical Society. 1974. Oct, 18(5): 307-319
  • Published : October 30, 1974
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Cho, Ung-In
Eu, Byung Chan

Abstract
The accuracy of the uniform WKB solution for a two-turning point problem is examined in comparison with the corresponding numerical solution. It is found that the uniform WKB solution is extremely accurate. Various Franck-Condon factors for a model system are calculated as an example of applications of such approximate wavefunction. The accuracy of the factors thus calculated is very good. By using the uniform WKB wavefunctions, we have examined the asymptotic limit of the Frank-Condon factors and derived the condition for the frequencies of the transitions, $E'_{n'J'}-U'_{eff}(r_s)=E"_{n"J"}-U"_{eff}(r_s),$, which was obtained by Mulliken using physical arguments