You can pick and choose what you'd like to learn about based on your interests. This is the most exciting part: you understand all of the fundamentals of undergraduate physics, and you can pick up advanced books in other topics of physics and will be able to understand them! You'll also be able to read and understand some papers on the arXiv , which is the place that almost all physics research papers are published. Graduate-level study in physics requires mastery of every topic within the Undergraduate Physics curriculum as covered above, and can be split into two categories: i the core courses and ii specialized coursework.
Graduate students typically take the core courses first, which cover the areas learned in undergraduate courses but in much greater depth and with far more mathematical rigor, and then choose more specialized courses depending on their area of research in physics. I'll cover each of these in the sections below. Note: many students are required to take a course in classical mechanics as part of the graduate core, but if you've mastered the material in undergraduate classical mechanics there is no need for this.
Studying electrodynamics, quantum mechanics, and stat mech in more depth at the graduate level requires a greater level of mathematical rigor. Graduate-level electrodynamics covers the same topics as undergraduate electrodynamics but with greater mathematical rigor. Graduate quantum mechanics is far more advanced than quantum mechanics at the undergraduate level. There are many things that you won't be able to understand about quantum mechanics at the undergraduate level that, after a little more mathematical training, you'll be able to understand once you get to this point.
Here you'll learn, in great depth, all there is to know about quantum mechanics, including quantum dynamics the Schrodinger equation , the Heisenberg picture , propagators , and Feynman path integrals , angular momentum , symmetries and conservation laws of the quantum world, perturbation theory , scattering theory , relativistic quantum mechanics , decoherence , and interpretations of quantum mechanics the Copenhagen vs.
Many-Worlds interpretations. Now that you have a more solid mathematical background and understand all of the fundamentals of quantum mechanics, it's time to approach graduate-level statistical mechanics. You'll revisit the Laws of Thermodynamics, and then pick up from where you left off in undergraduate statistical mechanics. Here, you'll revisit special relativity and the intricacies of spacetime , then learn the basics of differential geometry , how to deal with curvature , the essentials of gravitation , how black holes work, and the basics of cosmology.
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The whole idea behind QFT is that we are doing quantum mechanics on classical fields, and it works remarkably well. Along with GR, QFT will be the most challenging part of your physics education, but perhaps the most rewarding I know it was extraordinarily rewarding for me! It may take many, many years to master. You'll learn about how to quantize fields , Feynman diagrams , quantum electrodynamics QED , renormalization , non-Abelian gauge theories , quantum chromodynamics QCD , the Higgs mechanism , the Glashow-Weinberg-Salam theory of electroweak interactions, the symmetries of particle physics , and spontaneous symmetry breaking.
Please comment with your experiences and with any suggestions you have for improving this list! I had the honor of working with Bruce Schumm on a search for supersymmetry at the ATLAS detector, and he has one of those brilliant minds that understands physics so deeply that he can explain it to anyone without resorting to speculation. The Particle Odyssey by Frank Close : another brilliant popular introduction to particle physics and its history, beautifully illustrated with amazing figures and photographs.
Mathematical Preliminaries Before you begin studying physics and working through the topics in the sections below, you have to be familiar with some basic mathematics. Work through all of the "Mechanics" chapters in my edition, these are chapters This is the best introductory book I've found, and you can use it when you learn electrostatics and modern physics, too. It contains plenty of great example problems to work through, and the solutions are easy to find online. It does a great job of introducing the relevant mathematics, but you'll need to be learning calculus alongside it. Electrostatics What It's All About This is where you'll learn about the physics of electricity and magnetism electromagnetism in static situations situations where no motion is involved.
Work through the chapters on "Electromagnetism" in my edition, these are chapters You can find inexpensive copies of the 12th edition and the 13th edition.
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Waves and Vibrations What It's All About The mechanics of vibrations and waves are complex and important enough to demand their own course of study. These two books complement each other very well, and contain different problems and solutions. The Math You'll Need To Learn Alongside It By this point, you should have finished the introductory calculus books and are ready to move on to more advanced mathematics. Modern Physics What It's All About The fourth physics class that most undergraduates take is usually called "Modern Physics", and it's an introduction to topics in physics that will be taught in greater detail later in the undergraduate physics curriculum.
Work through the "Thermodynamics" section chapters in my edition of the book, and the "Modern Physics" section chapters Classical Mechanics What It's All About This is where you learn the real heart of classical mechanics, which you were introduced to in the very first topic Introduction to Mechanics. This is a fantastic introduction to classical mechanics. Morin's book is a good supplement to Taylor's, and contains some great problems to work through. Problems and Solutions in Introductory Mechanics by Morin supplement.
Even more great problems with solutions to work through, and contains some great problem-solving strategies. Kibble's Classical Mechanics supplement.
Another great book to supplement Taylor. A Student's Guide to Lagrangians and Hamiltonians supplement. This book can help you a lot if you get stuck on understanding the Lagrangian and Hamiltonian formalisms of classical mechanics. You need to master the Lagrangian and Hamiltonian formalisms if you want to understand quantum mechanics later on! The Math You'll Need To Learn Alongside It If you haven't finished working through Zill by now, you should master the topics in it by the time you finish studying classical mechanics.
Electrodynamics What It's All About Earlier, you learned about electrostatics: the study of static non-moving electricity and magnetism. This is a short textbook on vector calculus that is very helpful when trying to work with vectors in electrodynamics. Maxwell's equations are essential in understanding electrodynamics, and this book is the best supplement on the topic. It's written in the same concise and beautiful style, and every single problem is worth solving.
This is a really amazing, concise, and clear introduction to thermodynamics and statistical mechanics - the best I've found so far! A wonderful, fun, well-written introduction to astronomy that can be understood by anyone who has studied the first topic in undergraduate physics Introductory Mechanics. A super comprehensive introduction to modern astrophysics for students who are studying the undergraduate curriculum in physics.
Cosmology : Ryden's Introduction to Cosmology. My favorite introductory cosmology book! Accessible to anyone who has worked through the basics of electrodynamics. Written by the same Griffith who gave us the Introduction to Electrodynamics and Introduction to Quantum Mechanics , this book is the perfect introduction to the fundamentals of particle physics and is a joy to work through! Mathematical Methods in Physics What It's All About Studying electrodynamics, quantum mechanics, and stat mech in more depth at the graduate level requires a greater level of mathematical rigor.
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This book covers the essentials of everything you'll need to know for the mathematical rigor demanded by the graduate core. Visual Complex Analysis by Needham supplement. A light, fun summary of complex analysis that's concise, clear, and easy to read. Serves as a great supplement to the primary text when used along with Fisher's Complex Analysis see below. Tolstov's Fourier Series supplement. The best book on Fourier Analysis ever written. Complements the main text very well. Complex Analysis by Fisher supplement. Best when used along with Needham's Visual Complex Analysis to supplement the main text.
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Zee's Group Theory in a Nutshell for Physicists supplement. A brilliant introduction to group theory for physicists. Graduate Electrodynamics What It's All About Graduate-level electrodynamics covers the same topics as undergraduate electrodynamics but with greater mathematical rigor. This is the bible of classical electrodynamics, and everyone who works through either loves it or hates it I loved it.
If you can master everything in this book and work through every problem, you'll have mastered electrodynamics. Graduate Quantum Mechanics What It's All About Graduate quantum mechanics is far more advanced than quantum mechanics at the undergraduate level. This is my favorite textbook on quantum mechanics, and the one I used to learn quantum mechanics for the very first time. It's a wonderful, elegant, simple book with clear and understandable problems.
Try to work through all of the problems - if you do, you'll understand quantum mechanics very well. Quantum Mechanics and Path Integrals by Feynman essential. Sakurai's coverage of Feynman's Path Integral formalism of quantum mechanics doesn't do it justice. Working through this text written by Feynman himself is not only useful, but incredibly fun. Principles of Quantum Mechanics by Shankar supplement. A great supplement to Sakurai for more information about each topic.
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A bit too dense to serve as a primary text, it works best as an addition or reference. This book is very complex and you may not understand all of it even after working through Sakurai, but understanding decoherence is essential to understanding how the classical world arises from the quantum. This course covers differentiation, limits, finding maximum and minimum values, and continuity. There may well be some overlap with school mathematics, but the course is brisk and will go a long way quickly.
This course introduces the concepts of complex numbers, matrices and other basic notions of linear algebra over the real and complex numbers. This provides the necessary mathematical background for further study in mathematics, physics, computing science, chemistry and engineering.
Understanding electric and magnetic forces is of paramount importance for understanding the physical world. They are eventually responsible for the matter around us to self-organize in solid, liquid and gas phases , with given structures, density, elastic properties, and so on. Furthermore, they are responsible for light emission and propagation across the space. Already the first rudiments of electricity and magnetism will help to appreciate that they are two difference faces of the same coin: electromagnetism. This relationship is the first evidence of the possibility to build a unified description of the microscopic laws of the physical universe.