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.