How is the Compton scattering formula derived? Why is it that the position and momentum of a particle cannot be determined at the same time? At 19:00 on January 2, the seventeenth issue of "Zhang Chaoyang's Physics Class" began broadcasting. Zhang Chaoyang, founder, chairman of the board and CEO of Sohu, sat in the live video broadcast room of Sohu, first warmed up the past, then learned new, and used the law of conservation of energy and conservation of momentum to derive the Compton scattering formula, further proving the light quantum hypothesis. At the same time, de Broglie's material wave theory is also introduced, not only light has wave-particle duality, but also wave-particle duality, and lists experimental phenomena to prove the volatility of electrons; the width of the diffraction fringes of electronic single-slit is calculated, and the relationship between momentum and position uncertainty is in line with the Uncertainty Principle of Heisenberg measurement. It is also pointed out that heisenberg's uncertainty principle prevents the collapse of hydrogen atoms and estimates the radius of hydrogen atoms.
"For two consecutive lectures, we are hovering outside the gates of quantum mechanics." In the live broadcast room, Zhang Chaoyang summarized the lesson and the content to be talked about today in one sentence. "Let's first study the work of the great physicists between 1900 and 1930, all the problems they encountered." He emphasized, "Quantum mechanics is difficult to understand, and these examples should be repeated. ”
First warm up, then learn the new. "Zhang Chaoyang's Physics Lesson" has formed a personal character. Zhang Chaoyang reviewed the specific heat problem of the diatomic atoms in the live broadcast, the planck correction of blackbody radiation, and then talked about Einstein's revolutionary introduction of the concept of photons to explain the photoelectric effect, and once again explained the extremely magical wave-particle duality of light. At the end of the review, he said, "We continue to follow the trajectory of the work of those physicists of that year, further proving the photon properties of light." He then wrote the words "Compton Scattering" on a whiteboard.
Deriving Compton scattering experiments proves the light quantum hypothesis
(Zhang Chaoyang used the "small white board" to derive Compton scattering in the live broadcast)
Then, he took netizens to carefully deduce, through the joint conservation of energy, momentum x direction conservation, momentum y direction conservation, a total of three conservation equations, to solve the relationship between the wavelength of scattered photons and the scattering angle. Zhang Chaoyang said that for the two equations of conservation of momentum, the trigonometric relationship is used
The scattering angle of the electron can be eliminated φ to obtain:
For the equation of energy conservation, the relationship between the difference in frequency before and after the photon scattering and the difference in the dynamic mass before and after the electron scattering can be obtained by shifting the term so that the photon part and the electron part are on both sides of the equal sign:
After the two equations are eliminated, the formula describing the relationship between the wavelength of the scattered photon and the scattering angle can finally be obtained:
Zhang Chaoyang told netizens that Compton finished the experiment of photon and electron scattering, and found that the relationship between the wavelength change of the photon and the scattering angle in the experimental results was in line with the above formula, thus proving the correctness of Einstein's light quantum hypothesis.
Introduction to de Broglie waves Substances also have wave-particle duality
"But is it only the special substance of light that has wave-particle duality?" Zhang Chaoyang used a question to lead to another physicist who made great contributions to quantum mechanics, de Broglie. De Broglie pointed out that all matter has wave-particle duality, and analogous to the light-related formula, derived the material wave formula, which gives the relationship between the frequency of the material wave and the energy of the material particle, and the wavelength and the momentum of the particle.
(De Broglie formula)
Zhang Further explained that electron beams can diffraction like light or water waves. However, in most cases, because the wavelengths of common objects like tennis balls or people are too small, material waves cannot have a real impact on everyday activities. He pointed out, "And the electron diffraction experiment to be introduced next can prove the de Broglie wave formula very well." ”
The electron single-seam diffraction experiment conforms to the Heisenberg uncertainty principle
"All interference and diffraction have fluctuations", Zhang Chaoyang said, "In fact, in addition to the particle nature, electrons are also as volatile as light, so when the electron passes through a single slit, it will diffrraction due to its fluctuations, and we can calculate the diffraction fringes of the electrons like the diffraction of light." He goes on to introduce, "Diffraction of electrons can demonstrate Heisenberg's uncertainty principle. ”
In quantum mechanics, Heisenberg's uncertainty principle refers to the fact that it is impossible to determine the position and momentum of a particle at the same time, and the uncertainty of its position satisfies the relationship between the uncertainty of the momentum:
When the electron passes through a single seam, the uncertainty of the position of the electron can be known from the width of the seam, and the uncertainty of its momentum can be derived from the width of the diffraction fringe, and the uncertainty of the electron position is multiplied by the uncertainty of the momentum, which can be verified to meet the Heisenberg uncertainty principle.
(Zhang Chaoyang used the "small white board" in the live broadcast to illustrate the principle of electronic satisfaction of Heisenberg uncertainty)
At the end of the course, he stressed again, "We wandered outside the gates of the temple of quantum mechanics, gradually realizing the wave-particle duality of light; and realizing the wave-particle duality of electrons, and found that it can also diffraction; we also know the uncertainty principle, and we know that the position and momentum of particles cannot be strictly determined at the same time." Based on all this acquired knowledge, in the face of the mountain of quantum mechanics, Heisenberg used matrix mechanics and Schrödinger used wave equations to study in various ways, and finally ended up on the same path. ”
"We've used so many historical experimental phenomena to describe what microscopic particles are all about. Next, we will continue to go deeper along Schrödinger's path. In the next lecture, we will formally begin to study quantum mechanics, studying wave functions and Schrödinger equations. He told netizens about it.
Sohu video power knowledge live broadcast spread knowledge to play science
Since November 5, Zhang Chaoyang's Physics Class has been broadcast live for seventeen issues. In the first and second lessons, Zhang Chaoyang popularized "force" and "speed" and calculated the number of daily flight circles around the ground by Musk's spacecraft and the Chinese space station; the third and fourth lessons were related to "vibration", and the basic knowledge of visible light was popularized. Lessons five and six sparked a big discussion about the speed of sound and temperature. Revisit the two dark clouds of classical mechanics in Lessons VII, VIII, and IX; Lessons 10 and X11
Focusing on the blackbody radiation curve and its applications, Lessons 12, 13, and 14 attempt to enter the world of Einstein's thought, derive the famous formula "E=mc", and demonstrate the clock slow scale-down effect. Lesson 15 explains the structure of atoms and the decay of atomic nuclei. Lesson 16 is intended to discuss the wave-particle duality of light and to explore quantum mechanics. Lesson 17 focuses on Compton scattering and The Heisenberg uncertainty principle.
Observing life phenomena + explaining the principles behind + deducing the calculation formula, combined with the seventeenth physics class, it can be seen that "Zhang Chaoyang's Physics Class" is introduced from daily phenomena to help netizens understand the phenomenon, enhance interest, and then "see the essence through the phenomenon", explain the knowledge points, deduce the process, and in turn solve the problems in life.
In a follow-up course, Zhang Chaoyang will further explain the common physical phenomena in life. Through the topics that netizens are most familiar with, they can go deep and simple, explain phenomena, and explore the principles of the material world. Achieve the effect of professional recognition, ordinary people can understand, and thus stimulate the enthusiasm of scientific learning. The course is broadcast live on Sohu video every Friday and Sunday at 12:00.
In addition to "Zhang Chaoyang's Physics Class", Sohu Video also invited a number of general education broadcasters to popularize science knowledge and convey value. Dr. Chen Zheng, a teacher at the School of Science of Beijing Jiaotong University, played a "strange scientific experiment" and walked into the "wave-particle duality of light"; Bao Kun, a doctor of physical chemistry at Cornell University, incarnated as "Bao Daren playing science" to teach ordinary people to understand the 2021 Nobel Prize; and Liu Boyang, a doctor of astrophysics, popularized "How a total solar eclipse is produced". In the future, more knowledge broadcasters will settle in and play science together.