*Physics 751, 752 Michael Fowler,
*

**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.**