Simply put, when light is in motion, it can be regarded as composed of photons (particles) and particle-like, and its motion is transmitted in the form of waves, which is fluctuating.

More scientific and complicated statement:

wave-particle duality

Einstein was the first to affirm that light has both fluctuation and particle characteristics. He believes that electromagnetic radiation not only appears in the form of particles with energy hv when it is emitted and absorbed, but also in the form of particles when it moves in space. Einstein's brilliant idea was gradually formed in the process of studying the generation and transformation of radiation. At the same time, experimental physicists have put forward the same view relatively independently. Among them are W.H. Prague and A.H. Compton (Arthur Holly Compton,1892-1962). Compton proved that photons and electrons not only have energy conversion, but also have a certain momentum exchange in the interaction.

1923, de Broglie extended Einstein's wave-particle duality to microscopic particles and put forward the hypothesis of matter wave, which proved that microscopic particles also have fluctuations. His view was quickly confirmed by experiments such as electron diffraction.

Wave-particle duality is another leap in human understanding of the material world, which lays the foundation for the development of wave mechanics.

9. 1 Einstein's radiation theory

As early as 1905, Einstein implied the idea that fluctuations and particles are two forms of light in his optical quantum hypothesis. He analyzed the long-term debate between wave theory and particle theory since Newton and Huygens, pointed out the limitations of Maxwell's electromagnetic wave theory, reviewed Planck's thought of dealing with blackbody radiation, and summarized various phenomena related to the interaction between light and matter. He believes that the energy of light does not disperse in the process of propagation and interaction with matter, but appears one after another in the form of energy photons.

1June, 909, 65438+1October, Einstein once again wrote an article to discuss the radiation problem. In September, he gave a speech entitled "The development of our views on the nature and composition of radiation" at the 8 1 conference of German physicists and doctors held in Salzburg. He used the concept of energy fluctuation to study the motion of a complete mirror suspended in a cavity filled with thermal radiation at temperature t. If the mirror moves at a non-zero speed, the radiation with a given frequency v will reflect more from its front surface than from its back surface. Therefore, the motion of the mirror will be damped unless it gains new momentum from radiation fluctuation. Einstein deduced from Planck's energy distribution formula that the mean square fluctuation of the black body radiation in the volume V with the frequency between v→v+dv is

Then, Einstein explained the above two items respectively. The former term is the fluctuation of energy quantum, based on hν. The latter term has the form of electromagnetic field fluctuation obtained from Maxwell theory. The former represents particle properties and the latter represents volatility. Einstein declared: "these considerations ... show that the fluctuation of radiation spatial distribution and radiation pressure also behave as if radiation is composed of quanta of the above size." He stressed: "Modern radiation theory (referring to Maxwell's wave theory of light) is not consistent with this result." If (the first term) exists alone, it will lead to (expected) fluctuation, which occurs when the radiation consists of point quantum with energy hν. Einstein used the word "point quantum" to show that he had regarded light quantum as a particle. Although Einstein has not yet formed a complete radiation theory, he has clearly realized that radiation following Planck's energy distribution formula has the characteristics of particles and fluctuations at the same time.

In the above two papers, Einstein expressed the following views on the state of radiation theory:

"I have long intended to show that the existing foundation of radiation theory must be abandoned"; "I think the next stage of theoretical physics development will bring us the theory of light, which can be interpreted as the fusion of wave theory and emission theory;" "Don't put wave structure and quantum structure in the eye ... they are incompatible."

Einstein foresaw here that there would be a new theory to integrate volatility and particles, although he could not accept it when the new theory really appeared more than ten years later. Please refer the reader to the next chapter on this issue.

19 16, Einstein returned to the problem of radiation again and published the article "Quantum Theory of Radiation". This paper summarizes the achievements of quantum theory, points out the main defects of the old quantum theory, and demonstrates the quantum characteristics of radiation again by statistical methods.

The basic point he considered was that the stable distribution of discrete energy states of molecules was maintained by the constant energy exchange between molecules and radiation. He assumed that there are two basic ways of energy exchange, namely, the process of molecular transition, one is called spontaneous radiation and the other is called stimulated radiation. According to the probability of these two ways, he deduced Bohr's frequency law and Planck's energy distribution formula. In this way, he unified all the achievements of quantum theory in the previous stage into a logically complete whole. In particular, Einstein's stimulated radiation theory laid a theoretical foundation for the development of laser after 50 years.

In this paper, Einstein believes that in the process of interaction between molecules and radiation, there is not only energy transfer, but also momentum transfer. He assumed that in the direction of radiation beam propagation,

The momentum of hv/c is obtained, which has a clear direction. He wrote (2): "It seems that only when we regard those primitive processes as completely oriented processes can we get a consistent theory". "Because energy and impulse are always the most closely related", "that small effect (referring to impulse exchange) should be regarded as an obvious energy transfer caused by radiation."

192 1 year, Debye discussed Einstein's quantum radiation theory in a speech. As an example, he calculated the collision between photons and electrons, and the results showed that the wavelength of light became longer after the collision. At that time, he suggested his colleague P.Scherrer to do an X-ray experiment to see if the wavelength really changed. It's a pity that Schuler didn't do the experiment in time, so Debye temporarily put down his research. In the meantime, Compton has been trying to find a theoretical explanation for the experimental results of wavelength lengthening after X-ray scattering. Before introducing Compton's work, we should also mention another event related to wave-particle duality, that is, the debate between W.H. Prague and C.G.Barkla about the nature of X-rays.

9.2 Debate on the Nature of X-rays

X-ray fluctuation was found in the crystal diffraction experiment of Laue, Germany in 19 12. Before that, people had different views on the nature of X-rays. Roentgen tends to think that X-rays may be some kind of longitudinal wave in ether, and Stokes thinks that X-rays may be transverse ether pulses. Because X-rays can ionize gas molecules, J·J· Thomson also thinks it is a pulse wave.

Are X-rays waves or particles? Is it longitudinal wave or transverse wave? The most powerful criterion is the existence of interference and diffraction. In 1899, Haga and Wind put a well-made triangular slit in front of the X-ray tube to observe whether X-rays form diffraction fringes at the edge of the slit. On the one hand, they can't know the diffraction conditions in advance, on the other hand, it is convenient to measure the image broadening near the vertex. According to X-ray photos, if X-ray is a wave, its wavelength can only be less than 10-9 cm. This experiment was later improved by Walter and Pohl, and the photos obtained seem to have weak diffraction images. It was not until 19 12 that someone measured the photometric distribution of this photo and saw the real diffraction phenomenon. On this basis, sommerfeld calculated that the effective wavelength of X-ray is about 4× 10-9 cm.

Another effect of x-rays is quite obvious. When it shines on a substance, it will produce secondary radiation. This effect was discovered by Sagnac in 1897. Segnak noted that this secondary radiation is diffuse and is more easily absorbed than the incident X-rays. This discovery is a preparation for studying the properties of X-rays in the future. 1906, Bakla determined that X-rays were polarized. The experimental principle of Bakla is shown in Figure 9- 1. X-rays emitted from the X-ray tube are irradiated on the diffuser A at an angle of 45 degrees, and secondary radiation emitted from the diffuser A is projected on the diffuser B at an angle of 45 degrees. After observing the third radiation from all directions perpendicular to the secondary radiation, it is found that the intensity changes greatly. Along the direction perpendicular to the incident light and secondary radiation, the intensity is the weakest. From this, Bakla concluded that X-rays are polarized.

■ Figure 9- 1 Bakla Experimental Principle of X-ray Secondary Radiation

But polarization is not enough to determine whether X-rays are waves or particles. Because particles can also explain this phenomenon, as long as they are assumed to rotate. Sure enough, during the period of 1907-8, a debate about whether X-rays are waves or particles started between Bakla and Prague. According to the fact that gamma rays can ionize atoms, do not deflect in electric and magnetic fields, and have strong penetrating power, Prague claims that gamma rays are composed of neutral pairs-electrons and positive charges. Later, he treated X-rays in the same way and explained various known X-ray phenomena. Bakla insisted on the fluctuation of X-rays. The two men held their own opinions and debated in scientific journals. Both sides had some experimental facts to support them. Although the debate did not reach a clear conclusion, it left a deep impression on the scientific community.

In 19 12, Laue discovered X-ray diffraction, which provided the most powerful evidence for wave theory. Prague no longer insists on his neutral couple hypothesis. But he always intuitively thinks that, as he himself said, it seems that the problem is "not which theory is right, but to find a theory that can accommodate these two aspects." (1) Prague's thought has a certain influence on later de Broglie.

9.3 Compton effect

In the Physical Review of May 1923, A.H. Compton published the effect he found on the topic of the quantum theory of light element X-ray scattering, and explained it with the light quantum hypothesis. He wrote (2):

"From the point of view of quantum theory, it can be assumed that any special X-ray quantum is not scattered by all the electrons in the radiator, but consumes all its energy in a special electron, and this special electron scatters the ray in a special direction, which is at an angle with the incident beam. The curvature of the radiation quantum path leads to the change of momentum. As a result, the scattered electrons recoil, and the momentum is equal to the change of X-ray momentum. The energy of scattered rays is equal to the energy of incident rays minus the kinetic energy of recoil of scattered electrons. Since the scattered light should be a complete quantum, its frequency will also decrease proportionally with the energy. Therefore, according to quantum theory, we can predict that the wavelength of scattered radiation is greater than that of incident radiation, and "the intensity of scattered radiation is greater in the forward direction than in the reverse direction of the original X-ray, which is measured by experiments. "

Compton uses Figure 9-2 to explain the distribution of ray direction and intensity. According to the conservation of energy and momentum, considering the relativistic effect, the scattering wavelength is:

Δ λ is the difference between incident wavelength λ0 and scattering wavelength λ θ, h is Planck constant, c is the speed of light, m is the rest mass of electrons, and θ is the scattering angle.

■ Figure 9-2 Compton Theory Diagram

This simple reasoning has long been common sense for modern physicists, but Compton is hard to do. It took more than ten or twenty years to study this phenomenon, and Compton got the correct result at 1923. Compton himself took a detour for five years. This history shows the uneven course of the emergence and development of modern physics from one side.

It can be seen from the formula (9- 1) that the change of wavelength depends on θ and has nothing to do with λ0, that is, the absolute value of wavelength change is certain for a certain angle. The smaller the wavelength of incident light, the greater the relative value of wavelength change. Therefore, Compton effect is more significant for γ rays than for X rays. This has been the case in history. As early as 1904, British physicist A.S.Eve first discovered the signs of Compton effect when studying the absorption and scattering characteristics of gamma rays. His device is shown in Figure 9-3. The radiation and absorber in the picture are actually iron plates, aluminum plates and other materials. Radium tubes emit gamma rays, which are scattered by scatterers and then thrown into electrometer. Insert an absorber in the path of incident light or scattered light to test its penetration. Yves found that scattered light is usually "softer" than incident light.

Later, the scattering of gamma rays was studied by many people. In 19 10, D.C.H.Florance of Britain got a definite conclusion, and proved that the scattered secondary ray depends on the scattering angle, and has nothing to do with the material of the scatterer. The larger the scattering angle, the greater the absorption coefficient. The so-called light softening is actually that the wavelength of light has become longer. At that time, the essence of γ -ray was not yet determined, and it could only be expressed according to experimental phenomena.

■ Figure 9-3 Equipment of Yves Company (1904)

19 13, J.A.Gray of McGill University redone the gamma ray experiment, which confirmed rowlands's conclusion and further measured the radiation intensity accurately. He found: "The properties of monochromatic gamma rays will change after being scattered. The larger the scattering angle, the softer the scattered light. "

The experimental facts are clearly in front of physicists, but there is no correct explanation.

Compton also received γ scattering at 19 19. He measured the wavelength of γ -ray with accurate method, and determined the fact that the wavelength became longer after scattering. Later, he changed from gamma-ray scattering to x-ray scattering. Figure 9-4 is Compton's homemade X-ray spectrometer. After Kα ray of molybdenum is scattered by graphite crystal, the scattering intensity in different directions is measured by free cavity. Figure 9-5 is a partial curve published by Compton. As can be seen from the figure, the X-ray scattering curve obviously has two peaks, one is equal to the wavelength of the original ray (constant line) and the other is longer (variable line). The deviation between variable line and constant line changes with the change of scattering angle, and the greater the scattering angle, the greater the deviation.

■ Figure 9-4 Compton X-ray Spectrometer

Unfortunately, Compton, like others, took many detours to explain this phenomenon.

He first used J·J· Thomson's electron scattering theory to explain the scattering of γ -rays and X-rays, and later put forward the fluorescence radiation theory and the large electron model. He assumes that electrons have a certain size and shape, and thinks that as long as the radius of the charge distribution area of electrons is equivalent to the wavelength of γ-rays, the scattering of high-frequency radiation can be explained on the basis of classical electrodynamics. In order to explain why the frequency of fluorescent radiation becomes lower, he tried to use Doppler effect to calculate. In his calculation, he regarded the effect of X-rays on electrons in scattered matter as a quantum process. Start him.

This condition, in collision, should not only obey the conservation of energy, but also obey the conservation of momentum, which led to the publication of the historic document 1923 in Physical Review in May.

■ Figure 9-5 Part Curve published by Compton

Then, Debye also published a paper that had already been prepared. Their paper caused a strong response. However, this discovery was not immediately universally recognized by the scientific community, and a heated debate was quickly launched between Compton and his leaders. This happened after 1922. A Compton report on X-ray scattering must be discussed by a committee of the Physical Science Department of the American Research Council before it is delivered for publication. He is a member of this committee. However, W.Duane, the chairman of this committee, strongly opposed the inclusion of Compton's work, arguing that the experimental results were unreliable. Because Duane's lab is doing the same experiment, but it can't get the same result.

Wu, a Compton student, went to study in the United States from China, which made great contributions to the further study and verification of Compton effect. In addition to many convincing experiments on Duane's denial, he also confirmed the universality of Compton effect. He tested the X-ray scattering curves of various elements, and the results were in accordance with Compton's quantum scattering formula (9- 1). Figure 9-6 shows Compton and Wu.

A curve was published in Xun 1924, and the topic of the paper was: the wavelength of light element scattering molybdenum Kα line. They wrote: "The important thing about this picture is that the spectra obtained from various materials are almost identical in nature. In each case, the invariant line P appears at the same place as the fluorescence M0Kα line (the Kα spectral line of molybdenum), and the peak of the change line appears at the position M predicted by the above-mentioned quantum formula of wavelength change, which is within the allowable experimental error range. "

■ Figure 9-5 Part Curve published by Compton

■ Figure 9-6 Curve published by Compton and Wu in 1924.

Wu's most outstanding contribution to Compton effect lies in measuring the curve of the intensity ratio R of variable line and constant line with the atomic number of the scatterer in X-ray scattering, which confirms and develops Compton's quantum scattering theory.

Einstein played a particularly important role in affirming Compton effect. As mentioned earlier, Einstein further developed the optical quantum theory in 19 16. According to his suggestion, Bert and Geiger also tried to test who was right and wrong in classical theory and optical quantum theory with experiments, but both failed. When Einstein learned the results of Compton experiment in 1923, he enthusiastically publicized and praised Compton experiment in meetings and newspapers for many times and talked about its significance.

Einstein also reminded physicists to pay attention to: don't just see the particle nature of light. Compton relies on the fluctuation of X-ray to measure its wavelength in the experiment. He published a short article entitled Compton Experiment in the supplement of Berlin Daily on April 20 1924, with a sentence: "... the most important question is to consider how far we should go to give the properties of projectiles to particles or photons of light."

Thanks to the efforts of Einstein and others, the wave-particle duality of light quickly gained wide recognition.

9.4 De Broglie Hypothesis

As a prelude to quantum mechanics, Louis Broglie's theory of matter wave is of special importance.

De Broglie is a French physicist. He studies history and is interested in science. During World War I, I served in the army and worked in the radio station. I usually like reading scientific works, especially the works of Poincare, Lorenz and Langevin. Later, I became interested in the work of Planck, Einstein and Bohr, but turned to physics. After leaving the army, I studied for a doctorate in physics with Langevin. His brother Maurice de Broglie is an X-ray expert. Louis and Morris study X-rays together, and they often discuss related theoretical problems. Morris worked as a secretary at 19 1 1 the first solvay meeting, and was responsible for sorting out the documents. The theme of this conference is about radiation and quantum theory. The meeting documents inspired Louis a lot. Morris keeps close contact with another X-ray expert, W Prague. Prague once advocated the particle nature of X-rays. This view has a great influence on Morris, so he often discusses the relationship between waves and particles with his younger brother. These conditions urge De Broglie to think deeply about wave-particle duality.

The French physicist Brillouin published a series of papers during the period of1919-1922, and put forward a theory that can explain Bohr's steady-state orbital atomic meter. He imagined that the "ether" around the nucleus would excite a wave due to the movement of electrons, and these waves would interfere with each other. Only when the orbital radius of electrons is appropriate can a standing wave around the nucleus be formed, so the orbital radius is quantized. This view was absorbed by de Broglie, who removed the concept of ether and gave the fluctuation of ether directly to the electron itself, and made a deep discussion on atomic theory.

From September 1923 to October 10/kloc-0, De Broglie published three papers on wave and quantum in Bulletin of French Academy of Sciences. The first topic is "radiation wave and quantum". It is pointed out that physical particles also have wave-particle duality, and moving particles correspond to a sine wave, and they always remain in phase. Later, he called this imaginary immaterial wave phase wave. He considered the relativistic effect of moving particles with a rest mass of m0, and regarded the corresponding intrinsic energy m0c2 as a simple periodic phenomenon with a frequency of ν0. He applied the concept of phase wave to electrons moving around the nucleus in a closed orbit, and deduced Bohr quantization conditions. In the third paper entitled "Quantum Gas Motion Theory and Fermat Principle", he further proposed that "only the phase wave resonance is satisfied is the stable orbit." In the second year's doctoral thesis, he wrote more clearly: "The resonance condition is l=nλ, that is, the circumference of the electron orbit is an integer multiple of the phase wavelength."

In the second paper entitled "Optics-Optical Quantum, Diffraction and Interference", De Broglie put forward the following hypothesis: "Under certain conditions, any moving particle can be diffracted. Diffraction will occur when the electron group passes through a relatively small opening. It is in this respect that it is possible to find an experimental verification of our views. "

There are two points to explain here: first, De Broglie did not explicitly put forward the concept of material wave, but only used the concept of phase wave or phase wave, which is considered to be an imaginary immaterial wave. But what kind of waves are they? At the end of his doctoral thesis, he specifically stated: "I deliberately blurred the phase wave and the periodic phenomenon, just like the definition of light quantum, which can be said to be only an explanation, so it is best to regard this theory as a statement with unclear physical content, not a final theory." The matter wave was put forward by Schrodinger after the Schrodinger equation was established and the physical meaning of wave function was explained. Secondly, De Broglie did not explicitly put forward the relationship between wavelength λ and momentum P: λ=h/P(h is Planck constant), but later people found that this relationship was implicit in his paper, so it was called De Broglie formula.

De Broglie's doctoral thesis was highly praised by the defense committee as original, but people always felt that his ideas were too mysterious and not taken seriously. For example, at the defense meeting, someone asked what could verify this new concept. De Broglie replied: "The effect of this hypothetical fluctuation should be observed through the diffraction experiment of electrons on crystals." In his brother's laboratory, an experimental physicist, Willier, tried to do this experiment with a cathode ray tube. He gave up without success. Later, it was analyzed that the speed of electrons was not high enough, and the mica crystal as the target absorbed the free charge in the air. If the experimenter does it seriously, he will definitely make a result.

After de Broglie's paper was published, there was not much reaction at that time. It was Einstein's support that attracted people's attention later. Langevin once gave Einstein a copy of De Broglie's paper, and Einstein was very happy after seeing it. He didn't expect that his thought of wave-particle duality of light developed into such a rich content in De Broglie's hands and extended to moving particles. At that time, Einstein was writing a paper on quantum statistics, so he added a work introducing De Broglie. He wrote: "Mr. de Broglie has pointed out in a very noteworthy paper how matter particles or matter particle systems correspond to wave fields."

In this way, De Broglie's works immediately attracted everyone's attention.

9.5 Experimental Verification of Matter Wave Theory

As mentioned in the previous section, de Broglie once imagined that it was possible to observe the fluctuation of electron beam in the diffraction experiment of electron beam by crystal. I hope this foresight can come true. Intriguingly, there are two puzzling experimental results waiting for the correct explanation in theory. These two experiments are C W Ramsauer's electron-atom collision experiment and C J Davidson's electron scattering experiment.

19 13 years, the German physicist Jean Sauer developed an experimental method to study electron motion, which is called Jean Sauer's ring method. In this way, the velocity and energy of slow electrons can be determined with high accuracy. The concept of effective cross section of collision between particles was first put forward by Jean Sauer. After the First World War, Jean Sauer continued to use his ring method to carry out the experimental study on the atomic collision of slow electrons with various gases. 1920, he reported in an article entitled "the cross section of gas molecules to slow electrons" that he found that argon had special behavior.

The experimental device is shown in Figure 9-7.

Ransauer fills the chamber with different gases, such as hydrogen, helium, nitrogen and argon. After many measurements, he found that the cross section of general gas "tends to be constant with the decrease of electron velocity, but the cross section of argon becomes particularly small." From this abnormal behavior of argon, Jean Sauer concluded: "In this phenomenon, the slowest electron can freely penetrate into argon atoms."

Fig. 9-8 is the curve of the scattering cross section of inert gases Xe, Kr and Ar with the change of electron velocity, which was made by Ran Sauer according to the experimental results of many people. In the figure, the abscissa is the square root of the acceleration voltage proportional to the electron velocity, and the ordinate is the scattering cross section q in atomic units, where α0 is the Bohr atomic radius. The curve shapes of the three inert gases are roughly the same. When the electron energy is about 10eV, Q reaches the maximum and then begins to decrease. When the electron energy gradually decreases to about 65,438+0 ev, the minimum value of Q reappears. The energy decreases again and the q value rises again. Facts have proved conclusively that the elastic collision between low-energy electrons and atoms cannot be explained by classical theory.

■ Figure 9-7 Lanshore Ring Method

■9-8 Experimental Results of Ran Shaoer

This is the puzzling Ranshoer effect of that year.

Davidson's electron scattering experiment got strange results earlier than Ransauer's electron collision experiment. Davidson is a researcher in the engineering department of American Western Electric Company (later Bell Telephone Laboratory), engaged in the research of thermionic emission and secondary electron emission. 192 1 year, when he and his assistant Kunsman bombarded the nickel target with electron beams, they found that the secondary electrons reflected by the nickel target had a strange angular distribution, and the distribution curve was as shown in Figure 9-9, with two maxima. Davidson did not let this phenomenon go, tried again and again, and wrote an article in the journal Science of 192 1. His view at that time was that the appearance of the maximum might be a symbol of the electron layer, and this study might find another way to detect the atomic structure.