# 11.1 Schrodinger Spreadsheets

# SCHRODINGER SPREADSHEETS

*Physics 751, 752 Michael Fowler, University of Virginia*

**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.**

### Contributors

- Michael Fowler (Beams Professor, Department of Physics, University of Virginia)