Journal of the Korean Chemical Society (대한화학회지)

Korean Chemical Society (대한화학회)
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Uniform WKB Wavefunctions and Franck-Condon Factors

Uniform WKB 파동함수와 Franck-Condon 인수

  • Cho Ung-In (Department of Chemistry, McGill University) ;
  • Eu Byung Chan (Department of Chemistry, McGill University)
  • 조웅인 (카나다 McGill 대학교 화학과) ;
  • 유병찬 (카나다 McGill 대학교 화학과)
  • Published : 1974.10.30
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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.

2-전향점 문제의 Uniform WKB 파동함수의 정밀도를 대응하는 수치해와 비교하고 검토한 결과 Uniform WKB 파동함수가 대단히 정밀하다는 것을 발견하였다. 그러한 파동함수의 응용의 예로서 model계에 대한 Franck-Condon 인자들을 계산하였으며 계산된 인자들의 정밀도도 역시 매우 높다는 것을 보였다. Uniform WKB파동함수를 이용하여 Franck-Condon 인자의 점근치를 검토하였으며 전환진동수에 대한 Mulliken 의 조건, $E'_{n'J'}-U'_{eff}(r_s)=E"_{n"J"}-U"_{eff}(r_s),$ 을 유도하였다.

Keywords

References

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