How to become a Theoretical Physicist : A Textbook List for the Standard Physics Curriculum
Physics: Standard Textbooks
I here present a list of standard textbooks for the physics student. It is a compilation of books usually considered as being the “standard” or “classic” texts in physics. With this list, the motivated student can then confidently begin a self-study of undergraduate level physics or get started for an upcoming course. Now that I graduated, I want to share my experience with those students and I intend to write a series of hubs on some aspects that I sometimes found to be either misleading or difficult to grasp. I hope that with my help you’ll avoid the occasional pitfalls that I myself sometimes encountered.
How to become a Theoretical Physicist - An Advice
The basic topics in physics are easy to list : I have done it below. But the specific order in which your courses are to be taken is not so straightforward. If I may give this advice: do not blindly follow in order the suggested curriculum of your institution.
I often found that many students struggled with their physics homework not because they did not understand the physics, but because they could not do the maths. Mathematics is the ”tool kit” that physicists use in describing and analyzing physical phenomena. One just never knows what tools will be needed for a given job. This means that a physics major must have a wide ranging knowledge of different areas of mathematics, from differential equations, linear algebra and vector calculus to integral transforms, special functions, etc. These are the mathematics a physics major will encounter in courses in classical mechanics, electrodynamics and quantum mechanics.
Unfortunately, what typically happens is that students learn the mathematics at the same time they are learning the physics. This is an unfortunate way to learn the material, because more often than not, the mathematics gets in the way of understanding the physics. It is hard enough to learn the physics, but having to also learn the mathematics simultaneously makes the problem rather daunting. As an example, my Advanced Calculus (vector analysis) class was given afterElectromagnetism, where it is although much needed. So I had to learn the basics of vector analysis (the use of the grad, div & curl operators) in my EM class. And I'm glad I took Applied Analysis (Fourier transforms, etc.) before I had my first quantum mechanics course, even though it was a class usually given toward the end of the curriculum. The physical concepts to be learned in QM are already hard enough to grasp as they stand, without having to struggle to learn new mathematical concepts on top of that. (For those who might know what I'm talking about, let's say that wave packets became intuitive, and Fourier transforms made the swap between x-, p-representations easy to understand.)
So, as a rule, when I could do so, I tried to do my math courses first.
But one often cannot take those, either because the structure of the program makes it hardly possible, or because the student does not have the necessary prerequisites yet. If it's your case, hang on : the math you’ll learn in your physics classes should give you an edge (better grades) in the math classes that will follow. Still, a considerable amount of time can be spent on those mathematical matters that otherwise could’ve been spent on the physics. In the coming weeks, it is my intention to post short math summaries/tutorials/primers that can be conveniently studied as the need arise and will allow students to focus more on physics.
List of topics in physics and recommended physics textbooks
Here's a list of the basic topics in physics, with the books I recommend. These books are most probably offered at your institution. I agree, they are expensive. But (by clicking on the titles below) you can get them from amazon.com, where they are often cheaper (as a result of the high volume of books they order and sell).
Classical Mechanics Textbooks
by K.R. Symon. This is the standard undergraduate textbook on Mechanics. It covers a lot of topics (over 600 pages) and is packed with information. This book and Goldstein's Classical Mechanics is pretty much all you will ever need as a practicing physicist.
by J.B. Marion & S.T. Thornton.
Very Pedagogical...with an early (and easy!) presentation of lagrangian & hamiltonian dynamics. It also contains a chapter on variational calculus and another on nonlinear oscillations and chaos, something that is rarely seen in a book at this level. Used with Symon's Mechanics, it will enable you to become proficient at problem solving.
by H. Goldstein.
For over thirty years, this has been and is still the acknowledged standard in advanced classical mechanics. Period.
by D.J. Griffiths. It is a must have text for students new to the field; it features a clear, accessible treatment of the fundamentals of electromagnetic theory. Griffiths does an excellent job presenting the material in an easy to read, conversational manner.
by J.D. Jackson. The legendary book covering most of the physics and classical mathematics necessary to understand electromagnetic fields. There is nothing even remotely close to it in scope out there. It covers an enormous amount of material in a way that can be referred to later (post-course), including mathematical tools and explicit formulas. BUT it is very mathematically demanding, and some of the discussions (particularly towards the ends of chapters) are thoroughly inpenetrable. If you're going to use it, I recommend Wangsness (below) as an accompanying text.
by R.K. Wangsness. This book is a foundation that will give you the experience and confidence to tackle more difficult texts like Jackson. This was my first undergrad textbook on the subject, and I loved it. The mathematical formalism is at a higher level than Griffiths, but still, Wangsness doesn't gloss over the mathematical details: you can figure out all the steps. Every equation has a pointer to its predecessors so that you can trace back to the very beginning what has been done. It offers just the right blend of rigor and application; I like it because it gives you a methodic approach to problem solving. There are a lot of worked out examples; virtually all of the standard problems are included. It includes simple and standard examples solved with different methods, which permits comparison between those methods and will enhance your problem solving abilities.
Quantum Mechanics Textbooks
by D.J. Griffiths. It is the text to get if as a beginner you want to get acquainted with quantum mechanics. This is a problem-centered book and is accessible without serious prerequisites.
by R. Shankar. A marvelous book! Even tough it is a standard textbook, I unfortunately did not know about this one until after I graduated. My QM class would've been so much clearer with it... This book follows my "math first, then physics" philosophy (as Cohen-Tannoudji does - see below), with a self-contained introduction to the mathematics required to understand the content of the book. It also provides a section on Hamiltonian and Lagrangian mechanics, which the reader can either read through or skip and refer to later, without disrupting the continuity of the book. It covers Quantum mechanics fully and in a logical order. While the writing is concise, it is full of insightful observations. The explanations are clear and unassuming enough that if you had to, you could learn quantum mechanics just from this book, in spite of an incomprehensible professor. I warmly recommend it.
by J.J. Sakurai. This book makes an excellent follow-up to an introductory course on quantum mechanics. This is a theoretical-minded text, stressing the algebraic aspects of the theory. To read this book at the right level, you need to already know QM well enough to free yourself from the confines of the wave function, and think in terms of the state of a quantum system, with the wave function being its spatial incarnation. The concept of STATE, not wave function, IS the essence of quantum physics. The first three chapters (Fundamental Concepts, Quantum Dynamics, and Angular Momentum) of the book are wonderfully done. These chapters, I believe, were completed by Sakurai before his untimely passing. The rest of the book seems to lack Sakurai's clarity but it does an adequate job tackling this difficult subject.
by Cohen-Tannoudji, Diu & Laloe. The timeless reference by Nobel Prize Laureate Claude Cohen-Tannoudji. It first covers in detail the mathematical formalism of quantum mechanics and then presents a long and thourough overview of the physical foundations of quantum mechanics. It then goes on with harmonic oscillators, central potentials, scatterings, addition of angular momenta, perturbation theory, etc. A knowledge of vector calculus and linear algebra is assumed. This is the text I learned QM with. Although it is a very good text, it covers a wide range of subjects in a lot of details (it is a 2 volumes set), which is overwhelming for an undergrad. As an introduction, I would rather recommend Shankar (above); but as an advanced undergraduate or graduate text and a reference, it is excellent.
Thermodynamics / Statistical Mechanics Textbooks
by F. Reif. A classic. The author takes great pain to develop and elucidate a coherent physical picture for the edifice of statistical mechanics. However, if you are learning the subject for the first time, you might be too busy familiarizing yourself with the equations to be able to appreciate the value of his explanations and motivations. But then I still recommend this book as a complement to the one you use in class.
by C. Kittel. It is a standard book in thermodynamics. But I never used it, so I won't comment on it; I listed it here for your convenience.
Mathematical Methods of Physics
by Arfken & Weber. This is the standard book and the one you must have if you're a physics student. I suggest you get this one on your first semester, as you'll probably use it on a regular basis: it is very useful as a reference/companion book in everyday work. When you have to solve a concrete problem in physics, you do not want to spend a whole day looking through all your math textbooks. Now, with this book, you don't have to. It's also convenient because you can bring it with you everywhere. So, as a physics student, it is a must have. But if you want a book for self-study, I suggest Hassani's book (below). Topics: Vector Analysis, Vector Analysis in Curved Coordinates and Tensors, Determinants and Matrices, Group Theory, Infinite Series, Functions of a Complex Variable, The Gamma Function, Differential Equations, Sturm-Liouville Theory / Orthogonal Functions, Bessel/Legendre & other special functions, Fourier Series, Integral Transforms, Integral Equations, Calculus of Variations, Nonlinear Methods & Chaos, Probability.
by S. Hassani. The book gives a sort of enhanced recapitulation and new insights on the topics the reader already has a working knowledge of. Hassani goes right to the point and gets your attention right away; you cover a lot of stuff in a small amount of time. And when you get to the new topics, the rythm stays the same. How is it possible? With the use of easy examples. The goal of this book is not to become an expert on the topics of the book, but to get an overview of the mathematical methods you can apply to physics. The perfect book for a self-study. List of topics: Coordinate Systems and Vectors, Differentiation, Integration, Infinite Series, Integrals and Series as Functions, Dirac Delta Funtion, Vector Analysis, Complex Arithmetic, Complex Analysis, Differential Equations, Laplace's Equation and Other PDEs of Mathematical Physics, Nonlinear Dynamics and Chaos.
by S. Hassani. My favorite. This book is the first choice if you want to get a handle on the mathematical methods of theoretical physics at advanced undergraduate / beginning graduate level. The interconnections among the various topics are displayed by the use of vector spaces as a central unifying theme, recurring throughout the book. All the topics blend together in a wonderful, big unified whole...ahhhhhhh, joy!... The book covers: Finite- and Infinite-dimensional Vector Spaces, Complex Analysis, Differential Equations, Operators on Hilbert Spaces, Green's Functions, Groups and Manifolds, Lie Groups and Applications.
Most Widely Used Two-Year College Physics Textbooks
It's been 8 months since I published this article/hub. I'm now editing it to include a list of College physics textbooks. This list is taken from the American Institute of Physics (AIP) website.
I list them here for your conveniance, sorted in the usual calculus-based / algebra-trigo-based / conceptual categories.
Calculus based physics
by Raymond A. Serway
by Halliday, Resnick & Walker
by Young & Freedman
Algebra/Trigonometry based physics
by Serway & Faughn
by Cutnell & Johnson
by Wilson & Buffa
by Douglas C. Giancoli
by Paul G. Hewitt
by Kirkpatrick & Wheeler
[Note: English is not my native language. I welcome comments regarding my writing; if you find that an idea is unclear, that I should rephrase a sentence, or that I mispelled a word, please feel free to leave me a (constructive) comment to this effect. I would really appreciate it.]