Physics 751, 752 Michael Fowler,
For 751 Fall 2008: we will be using essentially this same material (approximately up to the lecture on the Density Matrix).
The assigned text for this course is Shankar, I also used
Sakurai (both books) for some of the later work, and occasionally
The following three lectures give a more detailed presentation of review material covered in the Introductory lecture.
Wave Equations, Wavepackets, Superposition PDF
Four Lectures on Essential Math:
Mostly One-Dimensional Quantum Mechanics:
1-D Schrödinger Equation: Examples PDF
General Uncertainty Principle PDF
Energy-Time Uncertainty
Principle PDF
The Simple Harmonic Oscillator PDF
Propagators and Representations PDF
Angular Momentum and Spin:
Orbital Eigenfunctions: 2-D
case PDF
Note on Curvilinear Coordinates PDF
Orbital Eigenfunctions in 3-D PDF
Undergraduate lectures: bosons
and fermions,
More on Angular Momentum:
Approximate methods:
Perturbation Theory:
Time-Independent
Perturbation Theory PDF
Two examples of Perturbation Theory:
Van
der Waals Forces between Atoms PDF
Time-Dependent Perturbation Theory:
The
Interaction Representation PDF
Time-Dependent
Perturbation Theory PDF
Applications to atom-light interactions:
The
Photoelectric Effect in Hydrogen PDF
Scattering Theory:
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)
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.