## Review of Physics

PHYS 6700X / Summer 2018

##

Organization

PHYS 67001— Review of Physics A: Mechanics & Thermodynamics (June 4 – June 22)

Prof. Boldizsar Janko

TA: Tae Kim

PHYS 67002— Review of Physics B: Electromagnetism (June 25 – July 13)

Prof. Anthony Hyder

TA: Tae Kim

PHYS 67003— Review of Physics C: Quantum Mechanics (July 16 – August 3)

Prof. Morten Eskildsen

TA: Luca Boccioli

Coordination and planning by the Director of Graduate Studies (Prof. Mark Caprio) and the Graduate

Curriculum Committee.

### Class

Monday – Friday, 9:00 AM – 11:30 AM, 184 NSH

-*Note: There will be no official class meetings on June 4, July 4, or August 3.*

### Office hours

The instructor will be available for afternoon office hours. The teaching assistant will hold

regularly scheduled afternoon help sessions.

## Description

### What is this course and why?

This “physics boot camp” for incoming graduate students is an opportunity for you to review

the essential components of your upper-level undergraduate physics courses, including classical

mechanics (with some thermodynamics), electromagnetism, and quantum mechanics. The goal is

to ensure that you and your colleagues have a common conceptual core, mathematical foundation,

and problem-solving proficiency as you embark on graduate studies.

It is important to realize that this is a “forward looking” review, designed to ease you into the mindset

of your core graduate courses and allow you to hit the ground running in the fall. For instance,

electromagnetism will focus on the application of Maxwell’s equations and wave dynamics, while

quantum mechanics will focus on properly understanding quantum mechanics in terms of state

vectors and operators living in Hilbert spaces. We have chosen textbooks at an appropriate level to

help you bridge this gap, and then, hopefully, to later serve you as resources in understanding the

classic but notoriously dense graduate texts.

A significant emphasis will be placed on ensuring you are fully at ease with the necessary (but, as

experience has shown, often spotty) mathematical background, such as vector analysis and linear

algebra. There will also be an emphasis on critical problem solving approaches, or how to decide

which approach to use and when to switch approaches, in order to help you with the transition

from the simpler undergraduate-level problems you may be familiar with to the more challenging,

open-ended problems you will find in your graduate courses.

Participation is optional, but highly recommended, since the material covered by the courses corresponds

to the requirements of the Preliminary Examination. We have redesigned our Preliminary

Examination to reinforce the goals of the summer course. The new Preliminary Examination consists

of three parts, split over three days, with subject matter corresponding to the three parts of

the summer course. If you have mastered the basic concepts and proficiencies of undergraduate

mechanics, thermodynamics, electromagnetism, and quantum mechanics, at the level covered in

the summer course, the intention is that you can expect to pass the Preliminary Examination on

your first attempt.

## Topics

### Review of Physics A: Mechanics & Thermodynamics

Statics (vector decomposition), central forces, rigid body motion, oscillatory motion and normal modes

Basics of Lagrangian/Hamiltonian formulation of classical mechanics

Laws of thermodynamics, ideal gas, state equation

Mathematical concepts reviewed include: Vector techniques and curvilinear coordinate systems;

derivatives, chain rule, integration by parts; total differentials, directional derivatives,

partial derivatives; basic ODE techniques (including exponential ansatz); Maxwell relations;

approaches for critically deciding among problem solving techniques and when to switch

among them

###

Review of Physics B: Electromagnetism

Basic electrostatics from the perspective of the Laplace/Poisson equation (e.g.,

Laplace/Poisson equation in simple geometries, image charges), multipole expansion, magnetostatics

Maxwell’s equations, electromagnetic waves, physical optics

Mathematical concepts reviewed include: Vector calculus for electromagnetism (gradient,

curl, Laplacian, vector derivative identities, vector integrals); basic linear PDEs (separation

of variables, exponential ansatz eikr & ei!t)

### Review of Physics C: Quantum Mechanics

General formalism of Hilbert spaces, matrix representation of quantum problems, coordinate/

momentum representations

Quantum harmonic oscillator (Dirac formulation), basic properties of angular momentum

operators, central force problem, identical particles

Mathematical concepts reviewed include: Linear algebra (matrices, vector spaces, eigenproblems);

eigenbases (including Fourier transform & series); linear operators (their representations

in various bases, commutator relations)

**Textbooks**

A principal text, indicated by an asterisk (*) below, has been identified for each course segment.

The department has purchased sufficient copies and placed them on reserve with the Chemstry/Physics Library so that you can check out your own copy for the entire summer. However, to allow you to obtain multiple perspectives on these topics, at the appropriate level, a variety of complementary textbooks are also being placed on reserve for each segment.

#### Review of Physics A: Mechanics & Thermodynamics

* John R. Taylor, *Classical Mechanics* (Univ. Science Books, 2005). ISBN 189138922X.

* Enrico Fermi, *Thermodynamics*, new ed. (Dover, 1956). ISBN 048660361X. [An e-book version is also available through the Notre Dame library.]

Herbert B. Callen, *Thermodynamics and an Introduction to Thermostatistics, 2ed*. (Wiley, 1985). ISBN 0471862568.

#### Review of Physics B: Electromagnetism

* J. R. Reitz, F. J. Milford, and R. W. Christy, *Foundations of Electromagnetic Theory, 4ed *(Addison Wesley Longman, 1993). ISBN 0201526247.

David J. Griffiths, *Introduction to Electrodynamics, 4ed* (Pearson, 2013). ISBN 0321856562.

Roald K. Wangsness,* Electromagnetic Fields, 2ed* (Wiley, 1986). ISBN 0471811866.

#### Review of Physics C: Quantum Mechanics

* David J. Griffiths, *Introduction to Quantum Mechanics, 2nd ed*. (Pearson Prentice Hall, 2005). ISBN 1107179866.

John S. Townsend, *A Modern Approach to Quantum Mechanics, 2ed* (Univ. Science Books, 2012). ISBN 1891389785.

Ramamurti Shankar, *Principles of Quantum Mechanics, 2ed* (Plenum, 1980). ISBN 0306447908.

Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalo¨e, *Quantum Mechanics, Volume I* (Wiley 1977). ISBN 0471164321.

**For all segments**

Riley, Hobson, and Bence will be your textbook for PHYS 70003 Mathematical Methods in Physics in the fall semester. You are expected to obtain your copy early, to use during the summer course, so that you can use it as a mathematical resource in the summer course. (Copies are available at the Notre Dame bookstore.) Your instructors will refer you to it for background and exercises on mathematical topics as needed.

K. F. Riley, M. P. Hobson, and S. J. Bence, *Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3ed* (Cambridge University Press, 2006). ISBN 0521679710.

## Practicalities

**Grading & attendance**

This course is graded satisfactory/unsatisfactory (S/U). If you come prepared and on time to the

class meetings and actively participate in the problem solving activities, you will get an S. Otherwise,

you will get a U.

Attendance is mandatory, and at most 3 absences are allowed from any of these course segment. If,

for any reason, you expect that you will need to be away for more than 3 of the 14 class meetings

of any of these segments, you are not eligible to register or receive a stipend for that segment. In

the event of unexpected medical or other emergencies resulting in absences beyond this limit, be

sure to notify the instructor immediately, and provide proper documentation. A course of action

will be determined in consultation with the DGS.

**Remote participation**

Even if you will not be here in time to formally enroll in the course, you are still invited to follow

along with the materials remotely to the extent your schedule permits. The instructor will post

all assignments online and may post additional resources as available. We will be setting up a

teleconferencing connection (via Zoom) so that you can observe the course on a live audio/video

feed and hopefully participate to a limited extent. If and when you do arrive on campus, you are

also welcome to join in person for the remaining class meetings.