Physics 751, 752  Michael Fowler, University of Virginia

Fourier Series

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.