Curve Crossing Problem with Arbitrary Coupling: Analytically Solvable Model

TL;DR

This paper presents an exact analytical method for solving the two-state curve crossing problem with arbitrary coupling, demonstrated on parabolic potentials with Gaussian interaction, impacting spectral calculations.

Contribution

It introduces a general analytical approach for the two-state curve crossing problem using Green's functions, applicable to arbitrary coupling scenarios.

Findings

Derived exact solutions for parabolic potentials with Gaussian coupling

Calculated effects of curve crossing on absorption spectra

Analyzed resonance Raman excitation profiles

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 potential. 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 electronic absorption spectrum and resonance Raman excitation profile.