Curve crossing problem with Gaussian type coupling: analytically solvable model

Abstract

We give a general method for finding an exact analytical solution for the two state curve crossing problem. The solution requires the knowledge of the Green's function for the motion on the uncoupled potentials. We use the method to find the solution of the problem in the case of parabolic potentials coupled by Gaussian interaction. Our method is applied to this model system to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.

Keywords:

• curve crossing
• quantum
• Green's function
• analytical model
• spectroscopy

Acknowledgements

One of the authors (A.C.) thanks Prof. K.L. Sebastian for valuable suggestions. A.C. would like to thank Prof. M.S. Child for his kind interest, suggestions and encouragement. The authors thanks Prof E.E. Nikitin and Prof. H. Nakamura for sending helpful reprints of their papers.