$$\require{cancel}$$

Physics 751, 752  Michael Fowler, University of Virginia

Fourier Series

Some Spreadsheet Illustrations of Scattering Theory Concepts

Phase Shifting by a Radial Square Well

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.)

Scattering Length for a Square Well or Barrier

Extrapolates the zero-energy straight-line wavefunction outside the well to see how it intercepts the axis.

(Page 415 of Sakurai.)

A Resonant State inside a Radial Square Barrier

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 Square Well Resonance Generated by the Centrifugal Barrier

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.

Resonance Shape with Background Phase Shift

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.