Resources

A Survival Guide for Core Graduate Physics Courses

By Jacob L. Beckey 06 July 2022

Introduction

If you are planning to enter a graduate program in physics in the US, it is fairly certain you will (if you haven't already) hear horror stories about John David Jackson's canonical graduate electrodynamics textbook (simply referred to as "Jackson"). To me, and decades of physicists that have come before me, Jackson is the archetype of a graduate textbook: exact and comprehensive, but extremely challenging to learn from. Many graduate texts, in general, focus on rigor and completeness at the expense of pedagogy. Perhaps this would be okay, if an expert researcher in a relevant field was the professor and helped the students understand the text throughout the course. Sadly, all-too-often, the aforementioned expert researcher is largely unable to communicate effectively to the novice student. So, if lectures don't seem to help and self-study is intractable, where should one turn? How, under these circumstances, could one hope to succeed in graduate school? The answer is simple: having several high quality supplemental resources is absolutely crucial for success in graduate school.

Thus, in this post I hope to construct just such a list for the courses which are almost always required in US physics graduate programs. Namely, I will suggest resources for: classical mechanics, quantum mechanics, electromagnetism, and statistical mechanics. I hope this list will benefit both struggling graduate students as well as motivated undergraduates that want to prepare for graduate studies. Personally, I find lengthy lists of resources somewhat overwhelming. The list that follows is not meant to be comprehensive, but rather contains many of the resources I used to get through the core courses at the University of Colorado, Boulder. Within each subsection, I attempt to order the resources by difficulty (from most accessible to least). Further, I will attempt to qualify each one when necessary. In general, though, they are all great and I hope you find them as useful as I did.

Classical Mechanics

Although surely not as "hip" as it was when Newton dropped the Principia back in 1687, classical mechanics ("class mech" for short) is an essential part of a graduate physics education. The fairly standard graduate text is by Goldstein and it can, compared to introductory courses on the subject, feel needlessly mathematical. In fact, a lot of graudate physics courses felt more like mathematical hazing than physics education to me. With that said, here are a few resources that helped me all the way through to the comprehensive physics exam.

  1. Leonard Susskind's Classical Mechanics (The Theoretical Minimum) : As you will see below, I highly recommend Susskind's books. Classical mechanics is the first book in a fantastic series. At best, though, it is just a highly enjoyable supplement to a real textbook. Regardless, I think it has a lot to offer in terms of setting a strong conceptual foundation for a more detailed study of the subject.
  2. Thornton and Marion's Classical Mechanics of Particles and Systems : Perhaps I am biased because I learned from this book in undergrad, but I found it to be very useful throughout my graduate class mech course. It has lots of canonical problems with explanations that serve as great supplements to graduate texts like Goldstein.
  3. David Tong's Notes You will see that my recommending Tong's writing is a general trend. In my opinion, there is not a more broadly useful resource than his lecture notes on theoretical physics. Essential reading for graduate students struggling through Goldstein or another graduate classical mechanics textbook.

Quantum Mechanics (QM)

Linear Algebra

If I could tell high school me one thing that would help him excel in physics, it would be to relentlessly study abstract linear algebra. I continue to be surprised by how ubiquitously useful linear algebra is throughout physics. In some places, it is extremely useful, in graduate QM, it is absolutely essential.

  1. Grant Sanderson's Essence of Linear Algebra Series: If you do not know 3blue1brown on YouTube, I cannot more highly recommend them. Their videos remind me why I love math and education. Specifically, his linear algebra series is a great visual overview of the subject.

  2. Sheldon Axler's Linear Algebra Done Right : The title says it all. If you understand this book cover to cover, you'll be (arguably) over-prepared for graduate QM. I was extremely excited when I stumbled upon several lectures from Axler's book by my favorite professor: Barton Zwiebach at MIT. If you are looking for a serious linear algebra crash course before starting graduate QM, Barton's lectures on linear algebra are the place to start.

    3. Undergraduate-level QM resources

    1. Leonard Susskind's Quantum Mechanics (The Theoretical Minimum) : Although this book is marketed as a somewhat popular text, it genuinely contains a lot of insight from the great theoretical physicist Leonard Susskind. Associated with each chapter is an online lecture which is great to review the reading. The main downside of the book, in my opinion, is lack of problems (though the few that are included are canonical). A particular strength of the book is the chapters on entanglement.
    2. Daniel A. Fleisch's A Student's Guide to the Schrodinger Equation : One of an excellent, growing series of student's guides published by Cambridge University Press, this book is pedagogical to its core. Fleisch takes the time to deeply explore the Schrodinger equation and its solutions in various canonical potentials. Overall, I think this book is a great supplement to chapter two of Griffiths (see below).
    3. David J. Griffiths' Introduction to Quantum Mechanics : This is one of the standard texts for undergraduate quantum mechanics courses in the US. Conversational, pedagogical, and nearly ubiquitous, Griffiths is a crucial companion for graduate quantum texts.

    Graduate-level QM resources

    1. Barton Zwiebach's Mastering Quantum Mechanics : I have never come across a more lucid presentation of quantum mechanics. Before being published as a full textbook, Zwiebach's lecture notes were available through MIT Open Courseware. The lecture recordings can be accessed on YouTube or through sites like edX. The quantum sequence at MIT (8.04, 8.05, 8.06) is famous thanks to Barton, and if you can master that sequence, you will excel in graduate courses.
    2. David Tong's Lectures on Quantum Mechanics: It seems there is very little David Tong does not know. His notes on countless subjects are immaculate and his quantum notes are no exception. Some may classify them as undergraduate, but I typically found them advanced enough to help with graduate quantum.
    3. Robert Littlejohn's Quantum Course at Berkeley: Another famous graduate quantum course with associated lectures. These are really at the level of Sakurai and other standard graduate texts. Both the notes and the lectures are pellucid but very advanced. The main downside is the lecture recordings are low quality. The penmanship, though, is remarkable.

    Electromagnetic Theory

    Here, I will group all of the recommendations together because my feel for what is and is not at the graduate level is far less well-defined for electromagnetism. Nonetheless, I will rank them from most accessible to least. Keep in mind, of course, that accessibility is a function of one's educational background. Just because someone says something is "supposed to be easy," doesn't mean it is. Such language is at best slightly helpful and at worst needlessly harmful.

    1. Daniel A. Fleisch's A Student's Guide to Maxwell's Equations :This book, and other books in the series, are really nice to have around. Maxwell's equations are so fundamental it pays to have a masterful understanding of them. This gentle guide helps the student develop that mastery.
    2. David J. Griffiths' Introduction to Electrodynamics : This is the standard undergraduate text on the topic. Always good to have around for the intuitive explanations. Griffiths includes a lot of what Jackson skips.
    3. Leonard Susskind's Special Relativity and Classical Field Theory (The Theoretical Minimum) : Susskind's most recent book in his Theoretical Minimum series is fairly advanced yet extremely accessible. It is most relevant for the field theory parts of Jackson. I consider it a gentle introduction to classical field theory and relativity. As with QM, Leonard has lectures online for each chapter.
    4. David Tong's Notes: Once again, Tong saves the day with immaculate lecture notes on vector calculus, electrodynamics, and even classical field theory.

    Conclusion

    Finally, I feel a certain obligation to recommend the Feynman Lectures on Physics. They carry a special status among physics texts. Feynman was a great explainer and the insights gained from reading them thoroughly will make you a better physicist. In particular, they are great when reviewing for graduate comprehensive exams. That said, it is comical to note that these lectures were delivered to freshman at Caltech... They are anything but an introductory text. That they are still so widely read today is a testament to their lasting quality.

    I used all of these resources to varying degrees throughout my first two years of graduate school and I suspect I will continue to use many of them for the rest of my learning and teaching career. The first year of graduate school is a daunting, overwhelming, and generally tiring experience. These resources, I hope, will make the tasks ahead seem a little more manageable. If I made it through courses, I guarantee you can too. My biggest piece of unsolicited advice is to make friends and bond over the difficulty of the courses. After all, I think that might be part of the reason professors still teach Jackson and the like. If nothing else, by completing courses that use Goldstein, Sakurai, and Jackson, you will gain the respect of previous physics students, people who know all-too-well how difficult these courses are.