# Cao Zexian New Year's Lecture: What is Quantum Mechanics?

1900 ~ 1928 was the most exciting era in the history of physics. A group of geniuses, mainly young people, constructed a brand-new quantum mechanics system in less than thirty years, which changed the face of physics.It has completely changed the face of human society. This report systematically explains what is quantum and mechanics. In the review of the creation process of quantum mechanics, it describes the specific content that constitutes quantum mechanics, and then introduces a few examples.The new technology brought by quantum mechanics will finally talk about how to learn quantum mechanics. Quantum mechanics has never been a revolution, it is only a natural and logical continuation of classical physics. Quantum mechanics, like other branches of physics, hasIt is the crystallization of human thought and wisdom. Quantum mechanics, and relativity, these brainstorms of a century ago should be the standard knowledge of educated people today.

On the evening of December 30, 2019, Cao Zexian, a researcher at the Institute of Physics of the Chinese Academy of Sciences, gave a multi-year scientific lecture "What is Quantum Mechanics?" In Physics.zhibo.sina.com.cn/tech/lzlx ".

Written by Cao Zexian Researcher, Institute of Physics, Chinese Academy of Sciences

Summary

Why study quantum mechanics?

What is quantum? What is mechanics?

What kind of science is quantum mechanics?

How was quantum mechanics created?

The power of quantum mechanics

How to learn quantum mechanics

Dear distinguished guests, friends in front of the screen, ladies and gentlemen, here is the Institute of Physics, Chinese Academy of Sciences, No. 8 South Third Street, Zhongguancun. I am Cao Zexian, an employee of the Institute of Physics. Next I want to talk to you about a tallOn the topic: What is quantum mechanics? Specifically, I will talk about why we study quantum mechanics, what is quantum, what is mechanics, what is the theory of quantum mechanics,The review of the establishment process introduces the specific content of quantum mechanics, talks about the power of quantum mechanics through a few examples, and finally I will talk about how to learn quantum mechanics. The people involved in the review of the establishment of quantum mechanics include Riemann and BoltzMann, Baltimore, Planck, Einstein, Sommerfeld, Leeds, Bohr, Heisenberg, Jordan, Born, De Broglie, Compton, Debye, Schrödinger, Pauli,Dirac, Von Neumann, Wigner, Concha, Bose, etc.

Many people will say that quantum mechanics is difficult to learn, but what I want to say is that quantum mechanics is not difficult to learn first; secondly, it is also difficult to learn. You may have noticed that I am standing here at the moment to talk about many corners of the worldSomeone here is using a mobile phone to watch the live broadcast. This was unimaginable a few years ago. In the past, Sun Wukong turned the river and the emperor Jade Emperor-that is the head of the gods, can only send clairvoyance and ears to see what is going on.Today, our human beings can use a telescope to survey the sky and overlook the entire earth in the sky. This is an era when technology surpasses mythology, and physics is the foundation of all technological progress. It used to be slow, slow to a lifetime, enough to learn to read a novel in its mother tongue.But in a highly developed era supported by science and technology today, the product of brainstorming in the last century, such as quantum mechanics, should perhaps become the standard for people's knowledge today.

Why do we study quantum mechanics? Quantum mechanics is simply a must-have for someone who is known to learn physics. Once upon a time, the French sage Poincaré said: "Although people are not happy because of science, they are not there now.Scientists ca n’t be happier. ”Similarly, we can say:“ Although people do n’t know that quantum mechanics is a physicist, but today ’s people who do not understand quantum mechanics claim to be physicists.May seem a little reckless! "Quantum mechanics and relativity are said to be the two pillars of modern physics! How can we not learn quantum mechanics as a pillar? Of course, the correct attitude should be to treat physics as an indivisibleOn the whole, we strive to learn from different directions and pursue a state of integration. People who study physics generally say that learning quantum mechanics makes us very happy. According to Dr. Sheldon in the American drama "Big Bang": "Quantum physicsmakes me so happy, it's like looking at the universe naked quantum physics makes me happy, The universe looks like streaking. "If you can learn some quantum mechanics in middle school, it's even better. Not only do you feel happy, you can also make your mother feel happy.

Figure 1. Dr. Sheldon: Quantum physics makes me so happy.

What is quantum? The positive, neutral, and negative forms of the Latin adjective "how much" are Quantus, Quantum, and Quanta, respectively. Today's English Quantity, quantity, and quantitative are related to quantity. They are quantitative and quantitative.Meaning. In Latin languages, such as Italian, what are the meanings of the cognate words of quantum, such as Quanto costano how much is this thing? Quanti anni hai how old are you? In English,Quantum has also been used as a “quantity.” Rainfall is a quantity of rainfall instead of a quantity of rainfall. There is an episode of quantum of solace in the famous 007 series, which is translated as “quantum crisis”. In fact, this is the same as “quantum”It has nothing to do with it. Quantum of solace means comfort and safety. In the past, when the special agents of the rivers and lakes went to any place, they must have the ability to quickly assess the safety of the environment. Nowadays, the language related to quantum mechanics in the WestIn this context, quantum quant is used as a noun singular, while quanta quanten is used as a noun plural, and occasionally it is useful.ntal. Quantum mechanics, the Japanese translate it into quantum mechanics, we are playing fiction.

What is quantum? It can be said that the smallest constituent unit of a thing is a quantum, which has integrity and indistinguishability. For example, the quantum of a fish school is a piece of fish. In the future we will know that abstract things, such as physicsThe amount of action, action, its quantum is Planck's constant h. When talking about the quantum world, we should pay attention to two words, atom and integer, do not simply understand them as "atoms" and "integer" according to the English-Chinese dictionary, no, theyThe correct meaning of the word should be understood literally. It is inseparable and unconnected in Latin. Our fingers and toes are separated and unconnected. To count them, use integer, 1, 2, 3, 4 ... theseDisconnected numbers. Based on such discrete objects is digital. We say that we are in the digital times, but digital comes from the word digitus, which means the fingers and toes. Atom and integer embody the quantumSpirit, this spirit is applied in daily life. During the Spring and Autumn Period, His Majesty Qi Jinggong had three fierce male grandsons, Tian Kaijiang, and Gu Yezi.Jugong's pride offended Xiang Guo Yanying "Yanzi passed by, and the three sons couldn't afford it", and the result was, "Once they were swearing, two peaches killed three men." Why can two peaches kill three men? Because peach is being eaten up by merits.In the context, there is an atomicity. Two peaches are divided into three people and they have to fight. The three warriors caused humiliation due to the fight, and they all committed suicide. This is completely a quantum scheme of others.Another example is that the People ’s Liberation Army has a lieutenant, General Pi Dingjun, who stated that “Eating eggs must be delivered to the soldiers in the form of boiled eggs, and no egg soup or scrambled eggs may be made.” Boiled eggs represent aThe existence of a separate egg, regardless of the difference in egg size, is eaten and eaten without any ambiguity. In contrast, eggs in the context of scrambled eggs and egg soup are mixed together, and the eggs lose their quantum characteristics.Then there is a lot of room for ambiguity: "Two pounds of egg fried two peppers and two pounds of pepper fried two eggs, both are peppers scrambled eggs." Quantum is the smallest unit of existence, for groups by a fewWe need to adopt a cautious attitude when talking about its system, because different methods or philosophies are used here. For example, in 2018, GDP was 93 trillion yuan, and the quantum expressed as RMB is9300 trillion points is a 16-digit number. We say that the growth rate is 6.6%, which is purely mathematically reasonable; in fact, it is 6.261245268932%. However, we say that the wage of a certain unit is higher than last year.If it is 6.61%, it may not be very scientific because it may be increased in several steps. The increase in salary is more related to personal matters. The vague and approximate 6.61% statement is not mathematically problematic but not scientific.If anyone mentions the population growth of the Lao Wang family, for example, the population of the Lao Wang family increased by 6.6%. Although it is only one decimal place, it does not seem to be human.In this case, it is appropriate to state clearly how many children the Pharaoh's family added to their children.Everyone should feel it at this time, the concept of quantum is not so evil, it exists in our daily life.

Figure 2. Two peaches kill three men, selected from "The Extract of Nanyang Han Portrait Stones"

So what does mechanics in quantum mechanics mean? Mechanics are machinery, bows and slingers are the earliest human machines, and mechanical watches are the pinnacle of mechanical manufacturing. Mechanics, mechanism, is about ingenuity, reason, and mechanism, how itgoes, similar to the Chinese word "Dao." Earlier people used the concept of machinery to understand various physical phenomena encountered, so the mechanics of heat, the mechanics of electricity, and atomicThe mechanics of atom. Mechanics is translated as a mistranslation of mechanics, mechanics in English is theory of force, and die Kraftslehre in German, but the concept of force has been kicked out of physics by Hertz in 1894, and laterPhysics basically does not use force to say things. Quantum Mechanics quantum mechanics, literally can be understood as the word about the world of small physical quantities.

Quantum mechanics is the product of a brainstorm of geniuses from 1900-1928. They almost all appear in this photo. This photo of the 5th Solvay Conference in 1927 is said to be the highest IQ and highest human history everThere is no one of them. The reason why these geniuses have such great achievements is that they are indeed geniuses; they did learn mathematics and physics early; they happened to be at that point in time and space. The fifth Sol in 1927The theme of the U.S. Conference was electrons and photons. That year, the term photon was coined the previous year. Electrons and light are quantum mechanics, of course, they are also relativity, the object of concern and the source of thought. I personally believe that "lightIt is the only connection between human beings and the distant place, the first physical object and tool! "Regarding the nature of light, people can understand it subconsciously.

On light, a song from the movie "Underground War" is particularly good. "The sun comes out and shines rays, geometric optics on the Quartet, Chairman Mao's mind flashes gold light color, spectroscopy light, and the sun shines on the body Thermal effect Hey, the brilliance of Chairman Mao's thoughts shines in our hearts light is an information carrier, and it shines in our hearts. "In just four sentences, the nature of light is fully described. And electrons, also called cathode rays,The beta particle was discovered in different ways in 1859-1909 and studied in various ways. It is responsible for many electrical properties of matter. Note that its discovery is always linked to light.

Figure 3. Group photo of participants in the 5th Solvay Conference in 1927

The concept of quantum, the first to go into science, was Riemann's 1854 paper? Ber die Hypothesen, welche der Geometrie zu Grunde liegen on the assumptions as a basis of geometry. In this paper Riemann proposedThe concept of manifolds, the differential geometry the mathematical foundation of general relativity, and the first use of quantum Quanta in science: "The part of the manifold that you want to distinguish by certain features or boundaries is called Quanta. Quanta's comparison is by its nature either a discrete quantity obtained by counting or a continuous quantity obtained by measurement. "

Figure 4. Screenshot of Riemann's 1854 thesis

Figure 5. Schematic diagram of blackbody radiation and spectral distribution obtained from experiments

1905, Albert Einstein 1879-1955 successfully explained the photoelectric effect using the hypothesis of the basic energy unit of radiation. He further assumed that the absorption of light by a solid is also performed by absorbing the entire unit of energy, so that it is emittedPhotoelectron kinetic energy is

, can well explain the measurement results of the photoelectric effect. At this point, the light has the energy unit dust settled! Later, Einstein also proposed that the energy unit of light and the momentum unit hν / c.

Figure 6. Photo of hydrogen spectrum

Figure 7. Schematic diagram of hydrogen spectrum

However, pay attention to the spectral lines. In addition to the position of the spectral lines, there are many problems such as brightness, width, fine structure, degeneracy, etc .. In 1925, 12 years later, in 1925, Göttingen assisted Born as an assistant.Werner Heisenberg 1901-1976 tried to answer the question of the intensity of the spectral lines, which led to matrix mechanics. Note that the spectral lines are related to two orbits, and the spectral line strengths should also be related to the two orbits. If a group ofThe energy is lined up, then lined up, and seeing the energy transitions between them, a matrix is obtained. Heisenberg tried to introduce the frequency from the Fourier expansion of the orbit and expressed it as the difference between the two terms.If it is determined that the spectral line is from oscillation, its intensity should be proportional to the square of the amplitude. Note that at this time Einstein has pointed out: "The concept of radiation intensity should be replaced by the concept of classic transition probability." Heisenberg willHis set of thoughts tried to find ideas on the harmonic oscillator and got the expressions of x 0 and p 0

1. W. Heisenberg, über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen quantum theoretical significance of the relationship between kinematics and mechanics, Z. Physik, 33 1925 879.

2. M. Born and P. Jordan, Zur Quantenmechanik on quantum mechanics, Z. Physik, 34 1925 858.

3. M. Born, W. Heisenberg, and P. Jordan, Zur Quantenmechanik II On Quantum Mechanics II, Z. Physik, 35 1926 557.

At the same time, British Dirac independently developed the theory of transition probability.

Quantity is a function of three variables or quantum numbers. In this way, quantum mechanics has a second form: wave dynamics. Schrödinger's article is titled Quantisierung als Eigenwertproblem.Deep meaning. The article is divided into four parts, namely Erste Mitteilung: Ann. Phys. 79, 361 1926; Zweite Mitteilung: Ann. Phys. 79, 489 1926; Dritte Mitteilung: Ann. Phys. 80, 437 1926; Vierte Mitteilung: Ann. Phys. 81, 109 1926.

By 1926, the particle nature of light and the wave nature of electrons were established, so chemist Gilber N. Lewis coined the term photon. In 1927, in 1927, Clinton Davisson 1881-1958 and Leather Lester Halbert Germer, 1896-1971 bombarded the Ni crystal with an electron beam. Born realized that the pattern was a result of the scattering of waves by the crystal. At this point, the wave properties of the electron were confirmed.

Figure 8. Photograph of particle track in a bubble chamber during photon bombardment of nucleus with electron-positron pair

On quantum mechanics, Eugene Wigner 1902-1995 is also to be mentioned. He and Weil 1885-1955 introduced group theory to quantum mechanics. With the group theory of quantum mechanicsIn order to understand the various characteristics of the spectrum, including the splitting of the spectral lines under the electric and magnetic fields Stark effect, Zeeman effect. From 1922 to 1925, Wigner first mentioned in his doctoral dissertation that the molecular excited state has energy broadening Δε, It is related to the average life Δt through the relationship Δε · Δt ~ h, and Heisenberg proposed that the uncertainty relationship of Δx · Δp ~ h was in 1927. Of course, there is no claim of uncertainty principleThose problems, such as the more accurate the particle position measurement, the less accurate the momentum. If you calculate the exact solution of the one-dimensional square potential well and the harmonic oscillator, you will find that the uncertainty of the position and momentum is positively correlated!

Weir was first a mathematician who contributed to quantum mechanics and relativity in his spare time. He also created gauge field theory. It is believed that Weir helped Schrodinger solve the Schrödinger equation for hydrogen atoms. Mathematicians like Weir didPhysics is more like physics.

1924, Indian Bose Satyendra Nath Bose, 1894–1974 also obtained the black body radiation formula on the assumption that the phase space has a volume unit h ^ 3. Einstein followed Bose's work and developedBose-Einstein statistics. Particles with integer spin all satisfy the Bose-Einstein statistics and are called bosons. Two German papers of Bose in 1924 1. SN Bose, Plancks Gesetz und LichtquantenhypothesePlanckian distribution and optical quantum hypothesis Z. Phys. 26, 178–181 1924. 2. SN Bose. W? Rmegleichgewicht im Strahlungsfeld bei Anwesenheit von Materie the existence of matter is the thermal equilibrium of the radiation field, Zeitschrift für Physik 27, 384-393 1924 were all translated by Einstein, this is a rare story in the history of science.

1926, John von Neumann 1903-1957 pointed out that the eigenstates of the operator are transformed into a vector space and named Hilbert space, and the quantum state can be regarded as HilbertA vector in special space; in 1932, von Neumann wrote the book "The Mathematical Basis of Quantum Mechanics."

So far, we have Schrödinger equation, Pauli equation and Dirac equation, Klein-Gordon equation, energy quantization hν, interaction quantity quantization h, and phase space quantization h3,Even if there is a large framework of quantum mechanics. Phase space quantization brings statistically significant quantum mechanics to quantum statistics. If you want to ask what is quantum mechanics, quantum mechanics is a physics composed of quantum mechanics equations and accompanying concepts and ideas.Theoretical system. Quantum mechanics is a crystallization of collective wisdom, a rare brainstorm burst in the history of human development. Nobel prizes in physics for contributions to the development of quantum mechanics include Planck 1918, Einstein 1922Obtained in 1921, Bohr 1922, Compton 1927, De Broglie 1929, Heisenberg 1932, Schrödinger and Dirac 1933, Pauli 1945, BohrEn 1954, etc. Among them, Einstein got the vacancy in 1921, Born finally won the prize as late as 1954, and these two are the key figures in the establishment of quantum mechanics.It ’s ridiculous to want to come

Reviewing the founding process of quantum mechanics, I found it to be a guess. Constructing quantum mechanics, or modern physics, is an art. In Born's words, it is the art of guessing the correct formula The art ofguessing correct formulae ~ Max Born. Some people will ask, is quantum mechanics objective, is quantum mechanics correct? I think this is a pseudo-question about objectivity. The physics of human beings depends on the physics of human beings and their relations withThe interaction between the environment is bound to be branded by people, and it is also branded by people of a particular era. The ancient Greek sage Xenophoni Ξενοφ? Νη? Said, "If a cow has a god, the god of the cow must have horns."It is conceivable that the car designed by crabs is destined to run rampant. How can we require that the quantum mechanics created by humans are objective? It must be more or less imprinted with humans.

Quantum mechanics is the brainstorming output of a group of geniuses. It should now be the standard knowledge of educated people, at least it should be the standard knowledge of middle school students. So how to learn quantum mechanics? If you focus on the history of creation, You can read Mehra's The historical development of quantum theory; if you are concerned about philosophy, you can read Jammer's The philosophy of quantum mechanics; if you are concerned about the founder's workbook, you can read Dirac's The Principles of quantum mechanics; ifIf you are concerned about the mathematics of quantum mechanics, you can read Von Neumann's Mathematical Foundations of quantum mechanics; if you are concerned about new theory of quantum mechanics, you can read about Lectures on quantum mechanics by Weinberg; if you are concerned with problem sets, you can read Practical Quantum of Flüggemechanics, if you pay attention to the most basic entry, you can read Cao Zexian's "Quantum Mechanics ~ Junior Edition".

Quantum mechanics is learned by measuring force, but in fact quantum mechanics is "difficult to learn, it is also easy to learn. People hold us!" I must emphasize again that quantum mechanics is a serious science and a natural continuation of classic physics. PeopleThe difficulty in learning quantum mechanics is mainly that you have not studied classical physics seriously. Before studying quantum mechanics, the following preparatory knowledge should have been learned or at least heard, including but not limited to classical mechanics, classical optics, electromagnetics, fluidsMechanics, thermodynamics, atomic physics, field theory, relativity ... Calculus, variation method, ordinary differential equation, mathematical equation, complex analysis, probability theory, Fourier analysis, linear algebra, group theory, invariant theory, etc.Wait.

Quantum physics makes me so happy. Learning quantum mechanics can also make my mother happy!

Enjoy it!

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