Modern Physics

Lecturer

Textbook

We are using the Feynman Lectures on Physics, a famous three-volume set used by physics majors at many institutions. We will be using chapters from Volumes I and III.

Overview

A typical modern physics course divides up into three roughly equal parts covering Special Relativity, Statistical Mechanics, and Quantum Mechanics. It covers the radical changes in viewpoint that occured between about 1900 and 1930.

None of those viewpoints have been so thoroughly overthrown as non-relativistic, classical physics was overthrown, so the ideas are the foundation for pretty much everything subsequent, including general relativity and quantum field theory.

Exams and Grading

There will be homework due every week. The homework will contribute 30% to the overall grade. Homework problems will be representative of exam problems, so if you miss a homework problem, it would be a good idea to understand why so that you are prepared if a similar problem shows up on the exam.

There will be one midterm during the week that the college designates as midterm week (October 19th-21st). For our class, that means the midterm will be on Tuesday, October 20th. The midterm will contribute 30% to the overall grade.

The final will be at the time that the college designates (8am-10am, Thursday, December 10th), the final will be cumulative, but since there is only one midterm, it will be weighted toward the material in the second half of the term. The final will contribute 40% to the overall grade. The cumulative part of the final will be take-home so you can focus on Quantum Mechanics.

Topics and Approximate Schedule

The course divides into three Units, with the first Unit including a review of mechanics and electromagnetism. As we review these subjects from freshman physics, we will introduce more advanced notation, and make sure that everyone has some familiarity, with unit vectors, the dot product, the cross product, and with the matrix and column vector representations for rotations and vectors.

The First Unit will cover Special Relativity as Feynman introduces it in Chapters 15 to 17 of Volume I. This is self-contained, simple and mind-bending.

In the Second Unit, we will cover Statistical Mechanics as Feynman introduces it in Chapters 39 to 41 of Volume I. Before Feynman covers Statistical Mechanics, he has to do a light introduction to Quantum Mechanics in Chapters 37 and 38 because there are some things in Statistical Mechanics that don't work at all without a little Quantum Mechanics. The principle failure of classical Statistical Mechanics is called the Ultraviolet Catastrophe, and we will definitely cover that.

For our Third Unit, which deepens the introduction to Quantum Mechanics we started in the Second Unit, we will cover much of Chapters 3, 4 and 7 of Feynman Volume III.

Detailed Schedule

Lectures	Topics
Sep 1	Review Newton's Laws of Motion and Newton's Law of Gravitation in Full Vector Form. Introduce and Use Unit Vectors. Review Gauss's Law in Integral Form.
Sep 3	Apply Gauss's Law to Spherical Charge Distributions. Introduce Unit Vectors in Polar Coordinates (r, theta, phi). Review Gauss's Law for Magnetism. Review Faraday's Law in Integral Form. Introduce Unit Vectors in Cylindrical Coordinates (r, theta, z). Review Lenz's Law and Right-Hand Rule by Demonstrating and Explaining Eddy Currents.
Sep 8	Review Ampere's Law. Repeat Maxwell's Gedankenexperiment that Demanded Maxwell's Addition to Ampere's Law. Review the Propagation of Light as a Self-Consistent Solution of Faraday's Law and Ampere's Law.
Sep 10	We derived the Time Dilation and Length Contraction Formulae by studying the Michelson-Morley Experiment.
Sep 15	We derived the Relativity of Simultaneity (the transformation equation for time) by utilizing the transformation equation for position and its inverse.
Sep 17	We derived the addition of velocities formula from the Lorentz transformation. We derived the local form of charge conservation from the integral form. The idea was to give you some idea of the relationship between Maxwell's Equations in Integral Form (as we reviewed them) and the same equations in Differential Form (as you will often see them on “Let there be Light” T-Shirts. Finally, we did Problem #5 from the Third Problem Set #3 in-class.
Sep 22	We derived all the algebraic properties of the rotation transformations. This was pretty intense as far as the amount of algebra I wrote up on the board, but it was made much simpler when we introduced some notation. We rewrote the results in terms of three-by-three matrices and operations on column vectors. We showed that the transpose of the rotation matrix is its inverse. We showed how the components of vectors transform.
Sep 24	We reviewed the results for the three-by-three rotation matrices from last time. We assembled the time and space coordinates into a four vector. Then we derived all the corresponding results for the four-by-four matrices that represent the Lorentz transformations. We defined the relativistic energy and momentum and showed that they can be put into a four-vector that transforms just like the time and space coordinates.
Sep 29	We closed out the First Unit by looking at some simple electric and magnetic situations in different frames. You will finish analyzing those situations and reconcile the viewpoints from different frames in the last Problem Set for Unit 1 (Problem Set #5).
Oct 1	We covered Feynman Chapter 37, which focuses on wave-particle duality and the electron double-slit experiment. We introduced the probability amplitude and the probability. To do this, we needed to introduce complex numbers and cover their basic properties.
Oct 6	We started a detailed example of probability amplitudes involving linear combinations of two particle-in-a-box wave functions. The probabilistic interpretation of the combination is that the particle is sloshing back and forth in the box. Email me if you want the Mathematica notebook containing the solution. A big part of the point of the example was to give you practice with complex numbers.
Oct 8	We covered Feynman Chapter 38. We skipped the section titled “Crystal Diffraction.” Problem Set #6 covering Chapters 37 and 38 went out as a PDF.
Oct 13	Having finished Feynman's lightweight Introduction to Quantum Mechanics, Chapters 37 and 38, we begin the Second Unit proper following Feynman's Introduction to Statistical Mechanics, by covering Feynman Chapter 39. We derived the ideal gas law formula from first principles. We also found a relationship between P and V for an ideal gas of photons that holds as you compress it. We found a similar relationship for an ideal gas of photons.
Oct 15	We prepped for the midterm by doing problems on special relativity, quantum mechanics and statistical mechanics.
Oct 20	Midterm
Oct 27	Chapter 40 of Feynman Volume I, especially the Maxwell-Boltzman Distribution.
Oct 29	Maxwell-Boltzman Continued and the Law of Atmospheres.
Nov 3	Chatper 41 of Feynman Volume I, especially equipartition. The Ultraviolet Catastrophe.
Nov 5	Discrete Energy Levels and Planck Black-Body Spectrum. Random walk, but did not get the time to do a decent job of Brownian Motion.
Nov 10	Go over Stat Mech Problem Sets (Problem Sets #7 and #8). Special emphasis on changes of variables in 1- 2- and 3-dimensional integrals. Begin the quantum mechanics unit. Discovered people have already forgotten the little intro to complex variables we did a few weeks back, so we'll re-do that.
Nov 12	Chapter 3 of Feynman Volume III. How are particles observed? Why are probability amplitudes complex? Reviewed properties of complex numbers, including commonly used identities, and representation in polar coordinates.
Nov 17	Begin quantitative two-slit interference, following Feynman's Sections 3-1 and 3-2.
Nov 19	Finish quantitative two-slit interference. Introduce Fermi and Bose statistics following Feynman Volume III, Section 3-4.
Nov 24	Particle in a box in 3-dimensions. Visualizing them. Showing that they satisfy Schrodinger's equation. State counting for fermions in a box.
Dec 1	Continue Fermi and Bose statistics for the many-particle casees following Feynman Volume III, Sections 4-1 and 4-2.
Dec 3	Time-dependent quantum mechanics, following Feynman Volume III, Chapter 7, Section 3.
Dec 10	Final, 8am-10am

Goals

We will have succeeded if you thoroughly understand the foundations of all three subjects — so well that you could turn around and teach them! — and you have a thirst for more. I'd consider myself to have failed if the course merely exposes you to a lot of advanced material which you are supposed to later get right in your upper-division courses.