The fourth part of the first series published "New Quantum World", which is very good! It's also my first promotion. There is a book "Ghosts in Atoms", which contains interviews in the late 1980s and debates about various interpretations. Read this book after a little understanding. It's good.
There is a book in the fulcrum series of Jilin People's Publishing House, where should the God of Destiny be placed-Dialysis Quantum Mechanics, which is a little philosophical and too short. It is not recommended to read it for the first time, but it is still good.
The only good book written by China people, History of Quantum Physics, is easy to find an electronic version on the Internet.
A professional book on historical development can read the History of Basic Particle Physics, which is very good.
The above are all popular books, and the difficulty is similar to that of The Universe in the Shell, with few formulas.
Some famous popular science masterpieces abroad: String of the Universe, From 1 to Infinity, New Quantum World and The Emperor's New Brain.
Reading popular science books is still amateur level. For a more professional introductory book, please read Fei Enman's Lectures on Physics (Volume III), which is easy to understand and can be studied in depth. Both students and teachers majoring in physics should read it.
The popular version of Feynman's lectures can be seen in Introduction to Feynman Physics, which extracts the popular introduction of quantum mechanics.
The most important thing in quantum mechanics is a clear grasp of concepts. Only by understanding the formal system and core concepts of quantum mechanics will you feel that quantum is so mysterious! Only by solving the problem will we not be unable to find the north. To really grasp its concept, we need to learn the knowledge of Hilbert space and Dirac symbol system, and the latter is the most important. A fool thinks:
1. The most important criteria for an excellent book on quantum mechanics are: explaining Hilbert space and a large number of spaces in simple terms, and thoroughly teaching Dirac symbols.
Second, we should clearly point out five or six basic principles or assumptions of quantum mechanics.
Third, key steps or concepts must be pointed out.
Let's analyze the popular textbooks in China according to the above principles.
1 Introduction to Zeng Quantum Mechanics
2 Zhou Shizhen's Quantum Mechanics
3 Yin Hongjun's Quantum Mechanics
4 Su Rukeng "Quantum Mechanics"
First of all, I want to say that there is not a textbook of elementary quantum mechanics in China to explain the concept clearly, especially the Introduction to Quantum Mechanics by Mr. Zeng of Peking University, which has a huge circulation and I used it when I was an undergraduate. Frankly speaking. There are few mistakes in it, but this is by no means the standard of a good book. For Dirac symbol, I wrote two pages, the language was vague, and the key points were hardly said. I think I don't quite understand even if P.A.M Dirac comes in person. As for Ceng Laoshi's quantum mechanics, it was the first one. The second volume is indeed very detailed, but the shortcomings are still the same. As a postgraduate teaching material, there is no complete theoretical system. Dictionaries can be used as reference books, but not as teaching materials.
The Quantum Mechanics written by Mr. Zhou Shizhun of Fudan University is much better than what he once wrote. Although a little old, it is more thorough and detailed. Of course, you don't have to keep pace with the times to deal with the postgraduate entrance examination. It's no problem to be older
Quantum Mechanics, edited by Mr. Yin Hongjun of HKUST, is a textbook for undergraduates and postgraduates, which is a bit difficult for undergraduates. There are many articles about Hilbert space and Dirac symbol, but unfortunately there is no main line. Besides, the arrangement is a bit messy and the printing is too poor. I wonder if the second edition (? ) Is there any improvement? I think it is good to modify it so that it is completely oriented to elementary quantum mechanics.
Fudan University, Mr. Su Rukeng's Quantum Mechanics is the best of the above books, with thorough explanation and wide coverage. Recently, I saw the higher education edition of Quantum Mechanics by Mr. Su in the bookstore. This book includes the content of postgraduate courses, and also says more about Dirac symbols. However, it is still not satisfactory. Using this book to understand quantum mechanics is basically a dream.
So far, the best introductory book about elementary or advanced quantum mechanics that I have read is the English version of Quantum Mechanics written by Cohen and others in France. Both the first volume and the first volume have Chinese translations, translated by Liu Jiamo and others. The thickness of this book is surprising. The first and second volumes of the English version are half a foot thick, but they look cool. The book is fluent and helps to improve English writing, hehe. And the text and supplementary articles are separated, beginners can choose to read, and the whole content starts from elementary quantum. In the second chapter, the knowledge of Hilbert space and Dirac symbol, the main mathematical tools of quantum mechanics, is described in detail and in simple terms. Note: The most important tool for learning the principles of quantum mechanics. I think it is: visualization of Hilbert space and clever use of Dirac symbol. By unifying the principle and mathematics, we can basically understand quantum mechanics. To understand "high volume", you hardly need to learn this book.
Note: Cohen is a very powerful physicist and a Nobel Prize winner. Together with Zhu Liwen and others, he won the Nobel Prize in 1997. And he missed a chance to win the prize decades ago, otherwise he would have won the prize twice.
Finally, I want to add that it is hopeless and impossible to understand quantum mechanics just by looking at the "initial quantity", because the initial quantity basically does not involve the knowledge of Hilbert space and Dirac symbol system. If you spend your energy on reading the first volume of an excellent high-volume book, you will soon master its essence. To tell the truth, it is best to read the classic original.
I don't think the knowledge of Hilbert space and Dirac symbols is abstract and difficult to understand. In view of their important understanding of quantum mechanics, I hope that the teachers of the Ministry of Education will revise the teaching syllabus of quantum mechanics for undergraduates and include the initial amount.
There are many high-quality masterpieces, most of which are from abroad. The four classical quantum novels are Neumann, Heisenberg, Pauli and Dirac. Dirac's Principles of Quantum Mechanics is the most famous, and it is called The Voice of the King. This is the only one I have ever seen. Among them, the fourth edition has a Chinese translation, translated by Chen Xianheng, with only over 300 pages. I suggest you look for it and make a copy. The essence of the book is (note: my views are not authoritative. The formal system of quantum physics is established, which unifies the formal expressions of different scenes and representations and emphasizes the formation process of physical ideas. In fact, after reading this book, I realized that the purpose of studying physics is to modify it, better express the laws of motion of the universe and transcend the shackles of human consciousness and experience. Haha, it's getting farther and farther.
Other famous textbooks are:
"Quantum mechanics, non-relativity." By Landau and Livershitz,
Schiff's Quantum Mechanics has a Chinese translation.
Landau's book, super classic, has been copied and hasn't been read yet. It's hard to say.
Schiff's quantum mechanics is also a masterpiece, which is very extensive and methodical.
The high-volume textbooks in China seem to be much better than the original ones. For example,
Advanced Quantum Mechanics by Mr. Ka Xinglin of Beijing Normal University,
Advanced Quantum Mechanics, co-authored by Mr. Ni Guangjiong and Mr. Chen of Fudan University,
Peking University Zhang Qiren's Quantum Mechanics,
Peking University Zeng's Two Volumes of Quantum Mechanics.
Advanced Quantum Mechanics by Mr. Yang Zesen
Mr. Zhang Yong's quantum mechanics,
Mr. xu zaixin's advanced quantum mechanics. wait for
Let's take a look at some of them.
Advanced Quantum Mechanics, written by teacher Ka Xinglin, is recommended as the first high-quality textbook in China. The mathematical exposition in the book is very rigorous and the logic is very clear. In the first and second chapters, the theoretical structures of Hilbert space and quantum mechanics are discussed respectively. What's more, the Dirac symbol is strictly analyzed on the mathematical basis of Hilbert space, which almost sweeps away all my doubts about the concept of quantum mechanics. That feeling is really wonderful! ! Mr. Ka is the chairman of the National Institute of Quantum Mechanics, which shows that his position in China is really worthy of the name. If we want to talk about shortcomings, I think this book is more suitable as the second volume textbook for physics graduate students. For the first time, we should choose a high volume textbook with less strict mathematical discussion and strong readability. Then read through Mr. Ka's Advanced Quantum Mechanics, and comprehensively sort out the concepts and systems. Teacher Ka has made great progress in operator algebra, which makes the book look good. In order to pursue the unity of form and logic, Mr. Ka didn't even write Feynman's path integral into the book, which is a little regrettable. But Feynman once wrote a monograph on path integral, which is easy to understand. You can read this book directly.
Advanced Quantum Mechanics, co-authored by Ni Guangjiong and Chen of Fudan University, is more advanced and uses less ink, which limits her readability. Maybe it's because my buddy is not good enough. The book contains a large number of frontier topics of modern quantum mechanics, and it has its own unique opinions on many issues, which is one of its great advantages. Generally speaking, it is not suitable for self-study as a teaching material.
Mr. Xu Zaixin's Advanced Quantum Mechanics is simple, easy to understand and fluent, but there are some shortcomings in scattering and relativistic quantum mechanics. Generally speaking, excellent introductory books, especially the first chapter (general description of quantum mechanics), can quickly grasp the essence of Dirac symbols.
Mr. Yang Zesen's Advanced Quantum Mechanics has long been heard to be extremely complicated, especially the chapter on scattering, which no one can understand. My buddy didn't believe me at first, so I took a look and it really lived up to its reputation.
The first and second volumes of Quantum Mechanics by Mr. Zeng Jinyan, as mentioned above, are a good reference book.
I have only read other books, but I haven't. Refer to other articles. For example, square.
Key concepts:
I. Hilbert space
1. The state vector emphasized in quantum mechanics is the so-called vector in Hilbert space. What is Hilbert space? Anyone who believes in linear space knows that Hilbert space is an inner product space that performs inner product operation on linear space and satisfies the completeness condition. Hilbert space used in quantum mechanics is Hilbert space over complex number field.
2. Hilbert space can be finite dimension, infinite dimension, continuous or discrete dimension and even irrational number dimension.
3. Simply put, the coordinate system describing the state vector is the so-called representation, and describing the evolution of the state vector over time is the description of the scene, such as Schrodinger's painting scene, Heisenberg's painting scene and Dirac's painting scene (interaction). Different paintings form different equations in different performances. For example, the expression of Schrodinger's paintings in the coordinate representation is the famous Schrodinger equation.
The same state vector has different representations in different representations, but it is the same vector in Hilbert space, just like the same vector in Euclidean space has different representations in different coordinate systems, and there are representation (coordinate) transformations between different representations (coordinate systems). The so-called unitary transformation. However, mechanical quantities are similar transformation relations in different representations.
As for the so-called wave function, I found that the concepts of wave function and state vector are indistinguishable in the initial quantity book. This is a mixture. Taking Zeng's book as an example, firstly, the probability amplitude is expressed by the wave function ψ (x), and its modulus is proportional to the occurrence probability. The so-called probability amplitude is an important concept, which represents the projection value of the state vector on a represented basis vector. (writing here, I found that I haven't explained the basic vector, 555555 ~, helpless! ! The modulus of probability amplitude is proportional to the probability of taking the eigenvalue of state vector through mechanics. On the other hand, ψ (x, t) is used to represent the state vectors, that is, the equivalent and right vectors, so the eigenvectors in are represented by coordinates.
ψ(x，t)| x & gt； It is more accurate to express. I was a little confused about this when I was in junior high school.
The basis vector is the common characteristic vector of a mechanical quantity or a group of mechanical quantities, which is orthogonal normalized. All the basis vectors of a mechanical quantity or a group of mechanical quantities are a representation in Hilbert space, which is a coordinate system in popular parlance. Mechanical quantity is a tensor in Hilbert space, which is generally second-order, that is, matrix.
Two. Dirac symbol
The advantage of Dirac symbol is that Hilbert space is divided into two dual spaces.
Use the right vector | α >; Represents the state vector, the vector on the left
& ltα|β& gt； Is the inner product and the value is a complex number. & ltα|α& gt； Greater than or equal to 0 is called modulus. Normalization is to use
|α& gt； be divided by
|β& gt； & ltα| is the outer product. This is an operator.
Use a, b, c, etc. To represent the operator, (a | α >; += & lt； α|A+, if A=A+, it is a self-adjoint operator.
(& ltα| A |α& gt； += & lt； α| A+|α& gt； = & ltα| A |α& gt； The expected value (average value) of the self-adjoint operator is a real number.
Note: the meanings of several expressions: | α >; Is the correct vector,; Represents a right vector,
& ltα| A |β& gt； Is a complex number, which can be considered as (
& ltα|(A |β& gt； ), that is, the inner product of a right vector and a left vector. This is a definition.
3. The basic principle of quantum mechanics:
Principle 1. The mathematical quantity describing the microscopic state is a vector in Hilbert space, and the difference between the two vectors is a complex factor, which describes the same state.
Principle two. It is the self-adjoint operator in Hilbert space that describes the micro-state physical quantity; The value of the physical quantity is, which is the eigenvalue of the corresponding operator; Physical quantity A is in state | ψ > Take the ai probability of each value, and the state vector |ψ > is based on the normalized feature vector of a {| ai >; | ai> is proportional to the complex square of the coefficient and to the complex square of ci in the following formula:
|ψ& gt； =∑| ai & gt； ci ci = & ltai |ψ& gt；
Collapse of wave packet: at | ψ >; State system, if the physical quantity A is measured to get the value ai, the system will enter the eigenstate | AI >； of A after measurement; .
Principle 3. The position operator x and the regular momentum p of particles in the microscopic system satisfy the reciprocity relation in rectangular coordinates:
[Xi Pj]=ih /2πδij
Principle 4. The change law of microscopic state with time is Schrodinger equation.
Principle 5. Describe the state vector of identical particles system. For the transformation of any pair of particles, namely boson and fermion, the state vector is symmetric and antisymmetric. Reflects the indistinguishability of the same particles.
The so-called superposition principle of states is well put forward by Mr. Ka. He not only emphasizes the relationship between superposition states and discrete states, but also emphasizes the differences between them. Dirac said: in the superposition state | ψ > a part of the system must be in | ψ 1 >; , some are in | ψ 2 > ...,
It can also be said that it is in a superposition state | ψ >; The system is neither | ψ1>; State, nor | ψ 2 > state, ..., is a new state.
That's all. These are mathematical tools and basic principles to understand the concept of quantum mechanics.
Formed a pattern of "one positive and seven deputy" of the central bank. Li Bo, former vice mayor of Chongqing, became the deputy governor of the central bank.