*Michael Fowler*

**Charged Particle in a
Magnetic Field PDF**

**Time-Independent Perturbation
Theory PDF **

**Van der
Waals Forces between Atoms PDF **

**The Interaction
Representation PDF**

**Time-Dependent Perturbation
Theory PDF **

**The Photoelectric
Effect in Hydrogen PDF**

**More Scattering Theory:
Partial Waves PDF **

**Yet More Scattering Theory PDF **

**Identical
Particles Revisited PDF**

*Not covered in
2007:*

**A Simple Example of Stationary
Phase Integration**

**More on Saddlepoints, and WKB
Connection Formulas**

**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.**