Phase space mapping for the harmonic model

The immediate objective is to obtain an analytic expression for vibrational overlap integrals, (vi vj). Conveniently, the integral over the product of the Airy functions can be shown (Connor, 1981) to be approximately another Airy function (in fact, rigorously true for linear potentials). If 

Note that the three factors mentioned at the beginning of this section as determining the size of (vi vj) appear explicitly in Eq. (5.1.12). The overlap integral contains 

---

Figure 5.4 Phase space mapping for the harmonic model. Two pairs of exactly degenerate interacting levels are shown. Since V2 is less steep than Vi, 0J2 < wi and (u( —Vi)< (v 2 — U2).

---