A projector formulation of the Van Vleck transformation. Part II. Near- Degenerate case.

What is it about?

(Uploaded: 2018-04-18). Part I is about the so-called degenerate case where all the perturbed energies in question arise from one single eigenvalue of the zeroth order Hamiltonian. Now we allow for a set of energies which lie close together (well separated from the remaining levels in zeroth order). We describe and compare three approaches for this near-degenerate situation: I: The formulas for the degenerate case can be used again if we replace the zeroth order energies with some mean value and adjust the perturbation accordingly. II: Adjustment of the hermitian operator S in the Van Vleck transformation exp(iS). III (Denominator corrections): Proceed first as with II, but S given by an expansion whose leading term is with use of I. NOTE: With Part I and II goes ERRATA (Mol. Phys. 1974, Vol. 28, 599) with 3 misprints in Part I and a left out formula in Part II.

Featured Image

Why is it important?

In applications within vibration-rotation spectroscopy the zeroth order Hamiltonian usually is the sum of harmonic oscillators with different frequencies. With these exited by varying numbers of quanta it can easily happen that some of these lie close together. We then talk about Fermi resonance. To obtain the rotational levels arising from such close-lying levels, the near degenerate approach is then appropriate.

Perspectives