Typical Feshbach resonances have certain simple properties.
The first is that the phase shift of the continuum wave function increases
by pi over an energy range covering the resonance. The resonance has an
energy width that depends on the coupling between the channels. The
"probability" for being in the resonance, integral of (y_closed)^2 over
all r, peaks at the resonance energy; the maximum of this probability
as a function of energy is inversely proportional to the energy width of
This is one frame from the movie. It shows the wave function in the open channel at one energy in the bottom graph, the wave function in the closed channel in the middle graph, and the energy dependence of the phase shift in the open channel in the top graph. The asterisk in the top graph shows which energy the frame is at. The movie shows a sequence of these frames with the only change being that the energy is incremented by a small amount in each successive frame. There are a number of interesting features to notice in the movie. The first is that for energies away from the resonance, -0.0061 or -0.0050, the wave function in the closed channel is small; it is only near the resonance energy that the closed channel function is large. The size of the wave function in the closed channel is proportional to the energy derivative of the phase. Notice the correlation between the wave function in the open channel and in the closed channel. Apparently, the continuum wave gets pulled in by one wave length when the energy increases through the resonance; this is the meaning of the phase increasing by pi.
Feshbach resonance movie, 1.5 Mb