Physics 751, 752 Michael Fowler, University of Virginia
Square Well Spreadsheet
Spherical Square Well Resonance Spreadsheet
Simple Harmonic Oscillator Spreadsheet
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.