**Classical Field Theory****Classical Mechanics****Class Notes****Classical Molecules****Miscellaneous Essays & Notebooks**

**Electrodynamics****Class Notes****Miscellaneous Essays**

**Mathematica Labs 2009**- A Remark Concerning These Notebooks.nb
- A. Contents, Index.nb
**C. Opened Manuals 2009 v.7****D. Exercises 2009 v.7**- Z. Notebook Management in Mathematica 7.nb

**Miscellaneous Math****Bell Polynomials, Pochhammer Symbols, Etc.****Biorthogonaloty & Spectral Decomposition****Borwein Walks Shrinking Steps**- Borwein & Shrinking Steps Text.pdf
**Graphics JPEG**- Walks Figure 1.jpg
- Walks Figure 2.jpg
- Walks Figure 3.jpg
- Walks Figure 4.jpg
- Walks Figure 5.jpg
- Walks Figure 6.jpg
- Walks Figure 7.jpg
- Walks Figure 8.jpg
- Walks Figure 9.jpg
- Walks Figure 10.jpg
- Walks Figure 11.jpg
- Walks Figure 12.jpg
- Walks Figure 13.jpg
- Walks Figure 14.jpg
- Walks Figure 15.jpg
- Walks Figure 16.jpg
- Walks Figure 17.jpg
- Walks Figure 18.jpg
- Walks Figure 19.jpg
- Walks Figure 20.jpg
- Walks Figure 21.jpg
- Walks Figure 22.jpg
- Walks Figure 23.jpg
- Walks Figure 24.jpg
- Walks Figure 25.jpg
- Walks Figure 26.jpg
- Walks Figure 27.jpg
- Walks Figure 28.jpg
- Walks Figure 29.jpg
- Walks Figure 30.jpg
- Walks Figure 31.jpg
- Walks Figure 32.jpg
- Walks Figure 33.jpg
- Walks Figure 33B.jpg
- Walks Figure 34.jpg
- Walks Figure 35.jpg
- Walks Figure 36.jpg
- Walks Figure 37.jpg
- Walks Figure 38.jpg
- Walks Figure 39.jpg
- Walks Figure 40.jpg

- Clifford Algebra.pdf
**Conway's Partitioned Disk Problem****Delta Functions****Differential Geometry**- A. Surfaces in 3-Space.pdf
- Asymptotic Ciurvature Matrix.pdf
**DINI SURFACES**- 1. Tractrix Construction.jpg
- 2. Tractrix & Catenary.jpg
- 3. Pseudosphere.jpg
- 4. Catecoid.jpg
- 5. Tractricoid & Its Evolute.jpg
- 6. Isothermal Coordinates.jpg
- 7. Helicoid.jpg
- 8. Dini Surface 1.jpg
- 9. Dini Surface 2.jpg
- 10. Bianchi Transform of Pseudosphere.jpg
- 11. Enneper's Surface.jpg
- 12. Breather 1.jpg
- 13. Breather 2.jpg
- 14. Breather 3.jpg
- 15. Breather 4.jpg
- 16. Breather 5.jpg
- 17. Strophoid of Revolution.jpg
- 17. Strophoid.jpg
**Surface of Revolution Geodesics**

**Geodesics on Surfaces**- Hexenhut as Tzitzeica Surface.pdf
**Tzitzeica Surfaces**

- Diffraction Problem.pdf
- Dove Prism & Dirac Spinor Spanner.pdf
- Dyson on Ramanujan Congruences.pdf
- Eigenvalues as Building Bricks..pdf
- Ellipsometry.pdf
- Factored Generating Functions.pdf
- Famous Unsolved Recursion Problems.pdf
**Fractional Calculus**- Fractional Permutations.pdf
**From Polynomial Generators to DEs**- Functional Determinants.pdf
**Functional Inversion Strategies**- Applied Functional Inversion .pdf
- Functional Inversion Addendum.pdf
**Functional Inversion Figures**

- Gaussian Integral Evaluation.pdf
- Generalized Pell Problem.pdf
- Generalized Resolution.pdf
- Generalized Spectral Decomposition.pdf
**Geometric Origin of Sine-Gordon**- Hannah's Problem.pdf
- Integrating Factor Construction.pdf
- Interpolation.pdf
- Jacobi Inversion & Mehler's Formula.pdf
- Kronecker Product.nb.pdf
**Lambert W Function Occurances**- Occurances of Lambert's Function.pdf
**Z. Associated Figures**

**Lambert W Function Sommerfeld**- A. Sommerfeld Final Text.pdf
**B1. Sommerfeld Figures**- Sommerfeld 1.jpg
- Sommerfeld 2.jpg
- Sommerfeld 3.jpg
- Sommerfeld 4.jpg
- Sommerfeld 5.jpg
- Sommerfeld 6.jpg
- Sommerfeld 7.jpg
- Sommerfeld 8.jpg
- Sommerfeld 9.jpg
- Sommerfeld 10.jpg
- Sommerfeld 11.jpg
- Sommerfeld 12.jpg
- Sommerfeld 13.jpg
- Sommerfeld 14.jpg
- Sommerfeld 15.jpg
- Sommerfeld 16.jpg
- Sommerfeld 17.jpg
- Sommerfeld 18.jpg
- Sommerfeld 19.jpg
- Sommerfeld 20.jpg
- Sommerfeld 21.jpg
- Sommerfeld 22.jpg
- Sommerfeld 23.jpg

**B2. Sommerfeld Addendum Figures 2**- New Addendum Figure 24.jpg
- New Addendum Figure 25.jpg
- New Addendum Figure 26.jpg
- New Addendum Figure 27.jpg
- New Addendum Figure 28.jpg
- New Addendum Figure 29.jpg
- New Addendum Figure 30.jpg
- New Addendum Figure 31.jpg
- New Addendum Figure 32.jpg
- New Addendum Figure 33.jpg
- New Addendum Figure 34.jpg
- New Addendum Figure 35.jpg
- New Addendum Figure 36.jpg
- New Addendum Figure 37.jpg
- New Addendum Figure 38.jpg
- New Addendum Figure 39.jpg
- New Addendum Figure 40.jpg
- New Addendum Figure 41.jpg

**Mathematica-based Materials**- Applied Frenet-Serret.nb
**Experimental MathPhysics Seminar**- Partitions of Unity-Ray's Argument.nb
**Random Walks**- Generalizations of Nest Command.nb
**Hexagonal Walks - Graphene**- Iteration Techniques.nb
- Random Walk.nb
- Random Walks in 2D.nb
**Resistance Distance & DC Circuits**

- Richard's Last Problem.nb
- Spectral Bounds.nb
- Unopened Seminar Slide Show.nb
- Wigner Semicircular Law.nb

- Meyer on Stein's Problem.pdf
- Multiplicative Partitions.pdf
- N-dimensional Frenet-Serret.pdf
- Nonstandard Mohr Constructions.pdf
- Novel Derivation of Newton's Identities.pdf
- On Lipsky's Markov Model.pdf
**Parrondo's Paradox****Parrondo's Game****Parrondo's Ratchet**- Test Parrondo.pdf

- Pythagoren Curiosities.pdf
**Random Walk on Hex Lattice**- Richard's Last Problem.pdf
- RigidModels.pdf
- Rotation Fields.pdf
- Single Slit Diffraction Problem.pdf
- Smooth Tensor Products.pdf
- Sphere-Kissing Problem.pdf
- Spherical Harmonics.pdf
- Square Gaussians.pdf
**Superoscillations**- 1. Berry's Construction.pdf
- 1b, Berry's Construction Figures.pdf
- 2. Superoscillations.pdf
**2b. Superoscillation Figures**- Figure 1.jpg
- Figure 2.jpg
- Figure 3a.jpg
- Figure 3b.jpg
- Figure 4a.jpg
- Figure 4b.jpg
- Figure 5.jpg
- Figure 6.jpg
- Figure 7.jpg
- Figure 8.jpg
- Figure 9.jpg
- Figure 10.jpg
- Figure 11.jpg
- Figure 12.jpg
- Figure 13.jpg
- Figure 14.jpg
- Figure 15.jpg
- Figure 16.jpg
- Figure 17.jpg
- Figure 18.jpg
- Figure 19.jpg
- Figure 20.jpg
- Figure 21.jpg

**Michael Berry Correspondence****Production of Berry Figures**

- The Maximal LCM Problem.pdf
- Time Of Flight Seminar.pdf
- Toy Perturbation Theory.pdf
- Trace of Inverted Matrix.pdf
- Uncommon Matrix Theory.pdf
- Unitary Bases.pdf
- Zeros of Perturbed Functions.pdf

**Quantum Mechanics****Class Notes****Mathematica Notebooks**- Dynamical Action Functions.nb
**Open Systems Seminar**- Partical-in-a-box Paradox.nb
**Quantum Lissajous & Vortices**- Quantum Walks on Graphs.nb
**Schmidt Decomposition & Purification**

**Miscellaneous Essays**- 2-Dimensional Hydrogen.pdf
- 2D Box Problems.pdf
- 2D Oscillator_Kepler to Wigner QM.pdf
**Angular Momentum, Spin**- Applied Theta Workshop.pdf
- Biorthogonality.pdf
- Box-like Wavepackets.pdf
**Boxed Wavepackers**- C of M in Classsical, Quantum Dynamics.pdf
- Causality_violation_by_localized_wave_packets (3).pdf
- Classical/Quantum Bouncer.pdf
- Density Matrix Transformations.pdf
- Ehrenfest's Theorem.pdf
- Energetics of a Gaussian.pdf
- Entanglement & the Separability Problem.nb
- Entanglement Seminar.pdf
**Free Will Theorem**- Gaussian Wavepackets.pdf
- Generalized Momentum Operators.pdf
**Generalized Quantum Measurement**- Imperfect Quantum Measurements.pdf
- Jacobi Inversion.pdf
- Loss & Recurrence 1.pdf
- Method of Sections.pdf
- Motion of Open Systems.pdf
- Motion of Reduced Density Operator.pdf
**New QM Perturbation Theory**- Normalization Problem.pdf
- Oscillator-Coherent States.pdf
**Partitions & Separability**- Phase Space in a Box.pdf
- Planck Centennial Fragment.pdf
- Q Measurement & Information.pdf
**Quantum Bouncer**- Quantum Master Equations.pdf
- Quantum Asymptotics Problem.pdf
- Quantum Misdemeanor.pdf
- Riccati Method in QM.pdf
- Schrödinger's Argument.pdf
- Schrödinger's Train of Thought.pdf
- Silverman's Quantum Question.pdf
- Smooth Tensor Products.pdf
- Spectral Coincidences in Hydrogen.pdf
- The Quantum-Classical Problem.pdf
- Toy Field Theory Seminar.pdf
- Unit Norm Condition.pdf
- Wavepacket in a Box 1.pdf
- Whittaker.pdf

**Quantum Simulations in Mathematica****Moving Expectation Values****No-Go Theorems, Bell & GHZ****Quantum Motion in Boxes**- Teleportation.nb

**Sophomore Class Notes 2007****Special Relativity****Thermo & Statistical Mechanics**

**Some remarks concerning the origins and nature of this material.**

I learned early on in my undergraduate education that while it is instructive to read, and to attend to the words of informed speakers, I cannot gain the feeling that I "understand" a subject until I have done my best to write about it. So much of my time these past sixty years—even when seemingly involved with other things—has been spent pondering the outlines of what I would write when I returned to my desk, "composing the next sentence."

Which means that I have been engaged more often in trying to write my way *to* understanding than *from* understanding. And explains why much that I write begins from (and frequently returns to) motivational remarks, and a survey of the surrounding landscape, but never with an abstract; when I undertake to write about a subject I have a head full of questions and hunches, but seldom a very clear sense of where my thought will take me. My "essays" have really the character of research notebooks—written on the fly, with little or no revision.

The patience of my readers is further tested by my tendency to digress, to "turn over rocks" as I encounter them, to see if anything interesting lurks under. And by the fact that too frequently my notebooks simply stop, without having been brought to a definitive conclusion...this sometimes because I acquired greater interest in some other subject, but more often because my attention was preempted by fresh classroom obligations.

When thinking through a subject in preparation for a class I have no option but to *write* my way through the subject, and then to lecture from my own notes. I find it much more pleasant and productive to spend an afternoon and evening writing than arguing with the absent author of a published text. And easy to entertain the delusion that what I have written is superior to the text. Inevitably it is at any rate different from any of the candidate textbooks, embodies organizational principles, analytical techniques and points of view that I prepared to "profess" (my responsibility as a professor) rather than simply to regurgitate/parrot. I suppose it is for that same set of reasons that many/most teachers of physics/mathematics (including all of those who influenced me most profoundly) prefer to work from notes.

For centuries, students have been proficient note-takers. But in the second week of my teaching career I was asked by students if I would be willing to distribute copies of my lecture notes. I was happy to do so (after all, imperfect note-taking distracted students from attending to and questioning my spoken words and blackboard squiggles), even though duplication technology was in 1963 still in a very primitive state of development. So came into being twenty-seven volumes of hand-written material (1963-1984), treating— sometimes in successive versions—all of the subjects standard to undergraduate physics curricula plus a variety of more advanced topics. At present the Reed College archivist is (at the recent instigation of Terry Lash, the student— now retired from directing the Nuclear Energy Division of the Department of Energy—who first asked me to distribute my notes) in process of digitizing that material.

In those early times my colleagues often adjusted their interests to conform to the capabilities of computers. This I refused to do. But in about 1990 I allowed Richard Crandall to "store" a NeXT computer (which would otherwise have escaped from the department) in my office. By that time, TeX (1986) and *Mathematica* (1988) were coming into use, and I discovered that personal computers were able to do at last what I wanted to do. Which made all the difference. I found myself positioned to do physics at a much deeper—and often more exploratory— level than ever before, and to write up and distribute it much more easily than had been possible with paper, pens (always several, with nibs of graded widths), ink and Xerox machines. And the whole exercise had become enormous fun!

I provide pdf versions of various class notes that were written in TeX after about 1995, but have not included the problem sets (which changed from year to year).

At some point in the early 1990s the department (on Richard Crandall's advice) adopted *Mathematica* as the computational language of instruction (displacing Pascal; the alternatives were Maple (1988) and MATLAB (1984)). In the fall of 2000 it fell my lot to teach the *Mathematica* labs (taught initially by Robert Reynolds, later by Rick Watkins) that displaced the first fall quarter of the experimental labs taken by sophomores. For that purpose I developed a set of seven autotutorial notebooks ("*Mathematica* for Physicists"), which were revised and modified as successive versions of *Mathematica* were released. To reenforce that experience, and to take advantage of the happy fact that my students could be expected to be comfortable with the software, I made increasingly heavy in-class use of *Mathematica*, first in my sophomore lectures, and later in more advanced (especially quantum mechanical) classes. And in my own exploratory work I more and more often generated notebooks, instead of TeX files. A few—but only a few—of those notebooks are reproduced here. All were either written in or adapted to run in v7. They run in v8 and v9, but I have discovered that v9 (maybe also v8) alters the format in a way that violates my original intentions; it does, however, provide a "Restore Original Format" button.

It had not been my intention to include the *Mathematica* lab notebooks, partly because they now appear to me to stand in need of major revision (some topics abbreviated or dropped altogether, others introduced in light of my more recent experience), and partly because they were intended by me to serve an educational objective that my former colleagues evidently do not embrace. But I do occasionally still get requests for this material, so have decided to include one version of the final (v7) edition. The labs were presented to students in "unopened" form: commands were presented, but the students themselves were asked to execute the commands and to ponder the results. Here I present the labs in "opened" form (commands already executed), and provide also the final edition of the exercises.