Quasiclassical selection of initial coordinates and momenta for a rotating Morse oscillator

Abstract

The classical orbits of a rotating Morse oscillator are calculated by means of Hamilton–Jacoby theory after truncating the Hamiltonian to permit analytical solution. Except at very high J, the approximate analytic orbit for the radial coordinate is in good agreement with that obtained by numerical integration of the exact equations of motion. Bohr quantization gives an expression for the rotation–vibration energy correct through quadratic terms in (v+1/2) and J (J+1), where v and J are the vibrational and rotational quantum numbers, respectively. The principal result is an analytic prescription for obtaining values of the coordinates and momenta, given v, J, and a set of random numbers, that facilitates properly weighted quasiclassical selection of initial states of diatomic molecules in trajectory calculations.