Physics 751, 752 Michael Fowler, University of Virginia
Some Spreadsheet Illustrations of Scattering Theory Concepts
This illustrates how the phase shift from a radial square well (or barrier) behaves as a function of energy.
(An animation of the diagrams on page 412 of Sakurai, for example.)
Extrapolates the zero-energy straight-line wavefunction outside the well to see how it intercepts the axis.
(Page 415 of Sakurai.)
Can be used to explore the relationship between resonances and bound states, and to see how the phase shift
increases on passing through a resonance.
A quantitative realization of the situation sketched on page 553 of Shankar. A square well can have a positive
energy sharp resonance, provided the angular momentum is nonzero.
A pole in the complex energy plane near the positive real axis gives a Lorentzian peak in the cross section,
reaching the unitarity limit. If there is a preexisting slowly varying background phase, there will be an energy
at which the scattering cross section is zero, and for a substantial background phase, this will be close to the peak.
In this spreadsheet, the background phase, set initially to zero, can be adjusted with the slidebar.