Semiclassical Theory of Inelastic Collisions. I. Classical Picture and Semiclassical Formulation

This series of papers is concerned with the derivation of the equations of the classical picture of atomic collisions, $i\hslash \frac{d}{\mathrm{dt}}{d}_i\mathrm{}\left(t\right)=\Sigma \stackrel{}{j}{h}_{\mathrm{ij}}\mathrm{}\left(t\right)\mathrm{}{d}_j\mathrm{}\left(t\right)\mathrm{},$ which describe the "time" dependence of electronic-quantum-state amplitudes as the nuclei move along a classical trajectory. These equations are derived in two ways. In the first formulation, which coincides with the intuitive classical picture of the collision, the nuclear part of the wave function is treated as a superposition of narrow wave packets, each traveling along a classical trajectory. In the second formulation, a semiclassical approach is used. The validity and meaning of the two formulations are discussed and compared.