The following is the senior brother's opinion:
Anyone who likes watching martial arts knows that practicing martial arts has internal skills and moves. In fact, learning physics is similar.
The internal strength corresponding to physics is mathematics. Presumably, all the younger brothers and sisters who studied electrodynamics in the second year of physics department have talked with Wang Xue (by the way, maybe you are lucky that Wang didn't come last semester). From the point of view of pure physics, once Maxwell's equations are established, there is little physics in them. But just for a little bit of the most pithy physics, we need a lot of practical mathematical tools, including four basic mathematical courses in physics department: advanced mathematics, complex variable function, mathematical equation and linear algebra. These are quite basic courses, and their importance is self-evident. But just learning these courses well is not enough for physics. I suggest that people who want to study physics take some more advanced courses.
Due to the limitation of teaching time, advanced mathematics doesn't involve many basic problems in "classical analysis". I suggest you read the New Lecture Notes on Mathematical Analysis written by Zhang Zhusheng of Peking University. At that time, I collected various versions of Mathematical Analysis, which was better than Zhang He's. Rich in content, suitable for self-study. Of course, don't forget the problem set of mathematical analysis of Peking University. Although this book is a complete set of mathematical analysis of the canal, there are many problems in it, which can make up for the shortcomings of the exercises in the book. I suggest you spend one year to one and a half years reading this set of books.
Complex variable function. I suggest you focus on its application, that is, knowing how to calculate. There are many theorems in complex variable function that correspond to each other in mathematical analysis, so it is not difficult. It is suggested that you learn theories other than "classical analysis" in complex variable functions, such as * * * shape mapping, as the basis for further study. I recommend Qintai Complex Variable Function of Beidazhuang. Maybe the front content is similar to that of Zhong Yuquan, but the back content is different. I haven't finished reading this book either.
Linear algebra. I suggest you read Advanced Algebra written by Wang Yifang and Ding. This is the textbook of advanced algebra in Tsinghua. This book teaches all the contents of Classical Algebra in a classic way, with rich exercises. It is very beneficial to study hard.
Mathematical and physical equations. I suggest you look at the mathematical and physical methods of Hilbert and Courand. This set of books is very concise and comprehensive. For students who have mastered "Classical Analysis" and "Classical Algebra", on the one hand, they can review almost everything they have learned, on the other hand, this set of books can be said to be a trump card for physics students, and so far it can be said to be "a small achievement". More importantly, a lot of content in this book has involved modern mathematics. In contrast, the books of Liang, Guo Dunren and Wang Zhuxi have their own strengths, but the realm has been purely applied. Of course, if you are proficient in one of these three books, it will also be considered a "small success".
I don't think it's easy to have such a "small success" in just four years, even though not many people had such a small success in the previous five years. There are often many people who start thinking about "great achievements" before "small achievements" and get nothing.
If you don't want to study math and physics, "Cheng Xiao" is enough. The key is to learn solid. For example, you don't have to know many theorems, but you must know the context and "roots" you have studied, so that you can draw inferences.
What I said above is only internal cultivation. There are moves to learn physics.
It is indisputable that learning physics should start with general physics. Through general physics, you can slowly feel what physics is, and thus really get started. Mechanics can choose the textbook of physics department, the set of green paper "Mechanics and Heat". Heat is selected from mechanics and heat. This set of books is easy to understand and comprehensive, and it is a good book for beginners. Electromagnetism can be selected from Zhao Kaihua's electromagnetism. This set of books is very classic and rich in content, which is a good guide to learning electrodynamics. Optics can be selected from Zhao Kaihua's Optics. Part of this book has gone beyond the level of general physics and should belong to the category of intermediate physics. It is a housekeeping book for optical students. As for quantum physics, it is difficult for me to find a satisfactory book, because there is almost no simple and correct explanation for quantum phenomena, so it is difficult to cover general physics.
As for the four mechanics, although they are a core of physics, I don't recommend beginners to learn them within four years, because they can be said to be profound, and even if they barely finish learning, they will not be proficient. For a bachelor of physics, I think it is not easy to master one of classical mechanics and electrodynamics. Classical mechanics can be selected from Landau's classical mechanics. This book is very thin, but it is the best in Landau's set. From Landau's discussion of Laplacian quantity, you can find that theoretical physics is not what you thought before. Electrodynamics can be selected from Guo's Electrodynamics. Reading Jackson's book requires a good mathematical foundation, and the key is to have a good understanding of potential partial differential equations. As for quantum mechanics and statistical mechanics, I don't think it is necessary for people who don't take physics as their profession. Electromechanics is not difficult to learn the electromagnetic field theory of electronic engineering; Classical mechanics is well learned, and it is easy to learn the vibration theory of machinery. Quantum mechanics and statistical mechanics are of little use outside physics. Therefore, for undergraduates who may not necessarily do physics in the future, it is better not to take such "useless" courses.
Having studied general physics, classical mechanics and electrodynamics, a bachelor's degree is enough. If you don't want to continue studying physics, you can learn something else. You will be surprised to find that because you have learned enough mathematics, other subjects are so easy, and their meticulous degree will not exceed that of classical mechanics and electrodynamics. If you intend to continue studying physics, you must study the most difficult quantum mechanics and statistical mechanics in physics. These two (actually one) subjects can be said to be inscrutable. Even for a person with small internal skills, their mathematics is beyond your control. In fact, many people try to turn quantum mechanics into "formal physics" like classical mechanics and electrodynamics, but such efforts always end in failure. The depth of these two subjects is far beyond the scope of our mathematics today.
Quantum mechanics is actually a quantum theory. It contains a wide range of contents, from the one-dimensional infinite potential that junior college students are very eager to learn to superstring, which can be said to be quantum theory. Quantum mechanics is roughly divided into two levels, non-relativistic quantum mechanics and quantum field theory and quantum gauge field theory. For the former, P.A.M Dirac wrote the famous principle of quantum mechanics in 1937. Learn from this book anyway. This book will tell you that quantum mechanics is not just a Schrodinger equation, but a set of principles. Starting from the principle, not from the specific problems, this is the real master approach. But there are too few exercises in Dirac's book. Please refer to Zeng's Quantum Mechanics I and II and Quantum Mechanics Problem Sets. Mr. Zeng overemphasized the rich content of quantum mechanics and neglected that quantum mechanics is first and foremost a set of basic principles, which is the deficiency of Mr. Zeng's book. But reading Dirac's Epiphany or reading Zeng's Epiphany leads to the same goal. But I think it's better to read Ceng Laoshi's books first and do more exercises. Otherwise, if you don't have enough understanding, you won't get anything just by reading Dirac's book. You can at least read Mr. Zeng's book first, lay a good foundation, and then read Dirac's book, and you will have an epiphany. But you have to understand that the quantum mechanics you are studying is "formal" and "unproven" from a mathematical point of view, and cannot be compared with classical mechanics and electrodynamics. In fact, people who study physics seldom care about this problem, but there is a book, Quantum Physics, which is discussed in detail. Although this book is called quantum physics, its content is the mathematical basis of quantum mechanics. But many of the concepts in it are the contents of modern mathematics, which looks very difficult.
The mathematical foundation of quantum field theory is not perfect, but as a "formal" theory, it has been applied more and more in physics in recent years. Those who engage in physics, especially theory, should learn to learn. The classic textbook is particle and field by Lu Rui. Starting with Dirac equation, this book is easily accepted by beginners, and it was written earlier, and there are many contents that are not available in popular books on quantum field theory. This can make beginners realize that we are trying and exploring under certain principles and many things are not taken for granted.
Quantum gauge field theory cannot be studied before learning Lie groups and Lie algebras.
It is not until you learn quantum field theory that you have the "root" of theoretical physics. The next thing depends on your interest.
If you are interested in condensed matter theory, you can study statistical mechanics. The books in this field are all based on Landau's books. Landau won the Nobel Prize for this. In his two volumes Statistical Mechanics, Landau explained the principles and methods of statistical physics clearly with the usual triviality of Russians (his classical mechanics is an exception). Of course, Landau is not complete. You can refer to Mr. Lake's modern statistical physics course. This book covers almost all the contents of statistical physics, but it is not clear. Fortunately, there is a reference. You can't learn condensed matter without studying solid state physics. I chose Huang Kun's solid state physics, which is easy to understand. During the Cultural Revolution, Master Huang also said that "learning (my) solid-state physics does not need to learn quantum mechanics"! However, he was criticizing quantum mechanics at that time. Huang Shi Fu Shuo said this sentence in order not to be implicated in solid physics. However, Mr. Huang's solid-state physics is really easy to understand and is a good teacher for beginners. As a condensed student, group theory is compulsory. But we studied the group representation theory. On learning groups, Sun Hongzhou's Group Theory (not Li Yuzhou) is enough. The content of group theory is roughly divided into two parts: finite groups and continuous groups. The former part is directly related to the symmetry of the crystal, and the latter part is related to the angular momentum theory, which is naturally used by people who study condensed matter when doing tight binding methods containing D or F electrons. If you want to do FANCY's condensed matter theory, you have to read FANCY's book. For example, Mahan's multi-particle problem (which should be translated in Chinese) or Green's function method in solid state physics of Peking University. However, it is better to read quantum field theory before reading these books, otherwise it will be more difficult. And as a transition, it is best to read Callaway's Theory of Solids first. However, it is not easy to understand the theory of solids. Tsinghua people is less.
If you are interested in optics, besides Zhao Kaihua's Optics, you should also read the classic works of optics. I hated optics at that time. I haven't read any books on optics. I always memorize the three-day formula before the exam. If you want to do quantum optics, then quantum field theory is useful. The trouble with quantum optics lies in the boundary conditions. The boundary of general quantum field theory is simple, but quantum optics is not. The quantum optical properties of finite systems are very interesting. Such as the absorption and emission of light in microcavity and some problems in photonic crystals derived from it. Here we should distinguish between photonic crystals and artificial dielectrics. Quantum effect exists in photonic crystals, but not in artificial dielectrics. Therefore, the ceramics with three-dimensional artificial periodic mechanism working in microwave band are not photonic crystals, but artificial dielectrics.
If you are interested in nuclear physics, I suggest you read more books on angular momentum theory or group theory. This is part of quantum mechanics. But the requirement of nuclear theory is to be extremely familiar with these things and use them whenever they can. These things are also very important for people who engage in quantum chemistry and energy band theory. But doing nuclear theory is hard, not as easy as condensed matter and optics.
People who are interested in the physical theory itself are afraid that "small achievements" in internal work are not enough. They need to study math further. We can start with real variable function and functional analysis. Learning real variable function helps you to establish some basic concepts of modern mathematics (such as function classes), master some basic methods and accumulate some materials. After learning the real variable function, you can enter the foundation of modern mathematics, functional analysis. Only by studying functional analysis can you have a clear understanding of (non-relativistic) quantum mechanics. At this time, quantum mechanics is not formal but strict. The best books on real variable function and functional analysis are real variable and abstract analysis.
In order to prepare differential geometry, we need to learn some topology and algebra. This is just a preparation concept, and it doesn't take much time. You can see blue algebra in the advanced algebra course. This book repeats the classical theory of matrix and linear space in the language of approximate algebra, which is very useful for understanding abstract algebraic concepts. Topology can be found in Fundamentals of Topology. There are many exercises in this book, but as long as the first chapter knows the other chapters, it is very simple.
After studying functional analysis and topology, you can learn differential geometry that is really useful in developing physical theory. The content of differential geometry is very complicated, from the most basic derivative value equal to tangent slope to geometry in function space. It is not easy to learn these in a short time, but there are traces to be found. The preferred introductory book is Chen's Fundamentals of Differential Geometry, which does not require a deep foundation, but it is an introduction to differential geometry. After learning, you can read Differential Geometry by Chen Shengshen. After reading these two books, go back to Differential Forms in Mathematical Physics and learn how to apply these mathematics. Differential Forms in Mathematical Physics is not a strict math book, but it is very good about how to use mathematics. If you think Lie groups and Lie algebras are useful, you can also read books on them. But I suggest looking for a book that introduces groups with special functions. After reading it, you will know how important it is to learn Bessel function and other mathematical methods. They are a direct reflection of symmetry, but you didn't realize it when you were young. After learning this, you will know what quantum mechanics really cares about. It turns out that quantum mechanics is a theory about symmetry. In this theory, the wave function of the base represented by a group is secondary, while the group itself and its eigenvalues are important. These physical quantities are eigenvalues.
If you go any further, you'll have to leave it to fate. Maybe you are lucky to find a way to combine quantum theory with general relativity, or maybe you are unfortunate to find nothing. This is the number of days, and it is useless to read more books.