Table of Content

10 September 2022 Volume 41 Issue 8

  

Study on the teaching of representation transformation theory in quantum mechanics: combining frontiers of neutrino oscillations

TU Tao, GUO Ao-lin, LI Chuan-feng, GUO Guang-can

College Physics. 2022, 41(8):  1.  doi:10.16854/j.cnki.1000-0712.210616

Abstract ( 576 )   PDF (911KB) ( 297 )  

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Quantum mechanics is a fundamental core course for undergraduate students in physics major, and its content is closely related to many research frontiers in modern physics. In this paper, we use the abstract formulas of representation transformation theory in quantum mechanics to study a specific case in the context of neutrino oscillations. In the teaching, we first introduce the flavor and mass representations of neutrinos, and then we can build up the representation transformation matrix between the two representations intuitively, where the matrix elements have a clear physical meaning: to represent the mixing angle between different neutrino mass eigenstates. Using this representation transformation theory, we can analyze the time evolution behavior of neutrinos and compare with the experimental neutrino oscillation phenomena. We found that the theoretical analysis can explain the experimental phenomena very well. The introduction of this cutting-edge example in teaching not only helps students to understand the representation transformation theory more intuitively, but also expands their horizons and stimulates their interest and enthusiasm for further research.

An approach to calculate the volume of three-dimensional reduced Brillouin zone

LI Jian-jun, ZHANG Zhen-dong

College Physics. 2022, 41(8):  7.  doi:10.16854/j.cnki.1000-0712.210521

Abstract ( 1069 )   PDF (839KB) ( 259 )  

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The solution of the volume of reduced Brillouin zone (BZ) is an important knowledge point in solid state physics. At present, the solution methods of BZ volume are generally different because of different BZ forms, which increases the teaching difficulty. In this paper, the reduced BZ is discretized into multiple pyramid with the origin of wave vector space as the common vertex, so that the solution of BZ volume is transformed into the sum of each pyramid. Taking the BZ volume solution of face-centered and body-centered cubic lattice as an example, it is obtained that the reduced BZ volume is the same as that of the reciprocal lattice primitive cell. The results show that the method is simple, intuitive and universal.

Systematic research on the movement of celestial bodies in the central gravitational field

ZHOU You, YU Xiao-xiao

College Physics. 2022, 41(8):  10.  doi:10.16854/j.cnki.1000-0712.210450

Abstract ( 521 )   PDF (934KB) ( 312 )  

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The motion of a celestial body around a central celestial body is to study the dynamics of two celestial bodies that can be regarded as particles under the action of universal gravitation. It is also the basic two body problem in celestial mechanics. Therefore, it is of great significance. In this paper, the motion of the central force field is simply solved by using the principle of conservation of mechanical energy. The orbit, speed and time of the celestial body moving around the central celestial body are systematically studied. The algebraic relations of orbit eccentricity, position coordinates, speed and time are established for the first time. At the same time, the derived formula has also passed the actual test of the orbit of Halley's comet, showing good accuracy.

Discussion on orbit angular momentum and rotation momentum in classical mechanics

LIN Zheng-zhe, CHEN Xi

College Physics. 2022, 41(8):  15.  doi:10.16854/j.cnki.1000-0712.210535

Abstract ( 630 )   PDF (839KB) ( 320 )  

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Angular momentum is an important concept in mechanics. In this paper, the concepts of orbit angular momentum and rotation momentum of a system of mass points are established in classical mechanics to make the theory more complete. The application significance is illustrated by several examples. Introducing orbit angular momentum and rotation momentum into classical mechanics can help students deepen their understanding of angular momentum, establish a relationship with orbit and spin angular momentum in quantum mechanics, and deeply understand the similarities and differences between spin angular momentum in classical and quantum mechanics.

Use matrix to study the relationship between  one-dimensional elastic collision and PI

YUE Guo-lian , HUANG Shao-shu , ZHOU Kui , ZHANG Li-chun , ZHAO Qing-wen

College Physics. 2022, 41(8):  19.  doi:10.16854/j.cnki.1000-0712.210350

Abstract ( 499 )   PDF (993KB) ( 305 )  

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This article uses a second-order matrix nth power to calculate the general expression of the velocity after the nth collision in a one-dimensional complete elastic collision. From this, the velocity after any collision is obtained. The collision velocity is divided into two cases. Based on the analysis, the corresponding relationship between the actual total number of collisions N and the pi is obtained. On this basis, the expression of the approximate calculation of the pi with the total number of collisions N and the mass ratio k of the two elastic sliders is derived.

Some applications of Lamé coefficient in mechanics

ZHOU Jian, MA Ying-han, MAO Ying-chen

College Physics. 2022, 41(8):  26.  doi:10.16854/j.cnki.1000-0712.210528

Abstract ( 640 )   PDF (826KB) ( 285 )  

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Based on the definition of Lamé coefficient, this paper calculates the Lamé coefficients in the commonly used orthogonal curvilinear coordinate systems, and gives the arc length, panel element and volume element represented by Lamé coefficient. Combined with specific problems, the application of Lamé coefficient in kinematics and analytical mechanics is discussed. Through analysis, it can be seen that the Lamé coefficient reveals the mathematical basis of one kind of physical problems, which is conducive to simplifying the understanding of this kind of problems and reducing the calculation steps. Furthermore, the use of the Lamé coefficient promotes the integration of related mechanics knowledge.

The study of electrostatic problems of the system consisting of charged rings and a conductor cylinder

YUAN Xiao-zhong, LIU Shi-yong

College Physics. 2022, 41(8):  30.  doi:10.16854/j.cnki.1000-0712.210571

Abstract ( 452 )   PDF (989KB) ( 249 )  

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The electrostatic system consisting of two uniformly charged identical rings and an infinite grounded conductor circular cylinder is studied. δ function is used to express the volume density function of the line charges in cylindrical coordinates．The Poisson equation with boundary condition is changed into Laplace equation and solved exactly.The potential distribution of the system is analyzed．The induced surface charge density on the inner surface of the cylinder is obtained from the potential distribution．The electric field produced by the induced charge along the axis of the system is calculated．It is found that because of the influence of the induced charge, the electrostatic force on a pair of point charges with the equal magnitude and the same sign on the axis is attractive under proper conditions．



On the linear transformation between inertial frames

GAO Qing, GONG Yun-gui

College Physics. 2022, 41(8):  35.  doi:10.16854/j.cnki.1000-0712.210623

Abstract ( 427 )   PDF (788KB) ( 264 )  

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 In most textbooks on mechanics, electrodynamics and relativity, the linear transformation between inertial frames is usually argued by the homogeneity and isotropy of spacetime. During teaching this subject, some students cannot understand this simple argument. After all, the science of physics should be explained with solid mathematics. This paper provides a solid mathematical proof of linear transformation between inertial frames based on the two postulates of special relativity and the homogeneity and isotropy of spacetime.



Further discussion on the principle of air exchange air heat engine

LU Jun-ling, GU Chen, REN Nai-jing, MA Bo-yi

College Physics. 2022, 41(8):  38.  doi:10.16854/j.cnki.1000-0712.210544

Abstract ( 404 )   PDF (1013KB) ( 169 )  

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The air exchange air heat engine is essentially a single piston heat engine. An expansion body (transposition piston) is rigidly connected with the piston in the cylinder. When the piston moves in the cylinder, the expansion body also moves together. At the same time, the air guide hole opened timely is set between the cylinder and the outside. The function of the expansion body is that its occupation forces the working medium air in the cylinder to change between the high and low temperature heat sources. When the air working medium begins to be compressed after passing through the high-temperature heat source, the air guide hole is opened, and the high-temperature air working medium in the cylinder is partially discharged out of the cylinder to reduce the resistance to the movement of the piston; When the air working medium begins to expand after passing through the low-temperature heat source, the air guide hole is opened, and the external air enters the cylinder through the small hole to increase the thrust to the piston. When the piston moves in the cylinder, the air guide hole is opened twice every cycle. The comprehensive effect is that the air working medium does positive work to the piston, which is shown as the state parameters of the air working medium on the PV diagram, and a positive cycle of the heat engine is completed.



Study of laser principle and technology experiment based  on external cavity surface emitting laser

GAI Lei

College Physics. 2022, 41(8):  42.  doi:10.16854 /j.cnki.1000-0712.210466

Abstract ( 414 )   PDF (1020KB) ( 179 )  

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Through building block experimental devices including pump light source,collimating and focusing system,gain chip,coupled output mirror,frequency doubling crystal and etalon,a comprehensive experiment of laser based on external cavity surface emitting laser are established.The basic principle of laser,frequency change technology,wavelength tuning technology and other experimental contents have been completed.For this experiment,the related contents of laser technology are synthesized,advanced scientific research theory knowledge with experimental practice is combined,and a variety of designed experimental contents is provided to give students autonomy in learning so as to achieve the purpose of promoting experimental teaching.

A demonstration experiment of piezoelectric effects

XIAN Fu-zheng, , WANG Chun-ming,

College Physics. 2022, 41(8):  47.  doi:10.16854/j.cnki.1000-0712.210477

Abstract ( 483 )   PDF (1161KB) ( 182 )  

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The experimental device and scheme are designed to demonstrate the positive and inverse piezoelectric effects, in which the coupling relationships between mechanical energy and electrical energy are studied. A drive signal is applied to an electromagnet to stimulate vibration of piezoelectric bimorph. Both drive signal and generated electric signal are measured by an oscilloscope. Electric signal frequency is consistent with drive signal frequency, while electric signal amplitude is positively correlated to drive signal amplitude. Electric signal amplitude first increases and then decreases with drive signal frequency. The piezoelectric bimorph is excited by DC voltage source to produce deformation, which is amplified by an optical lever. The displacement of the piezoelectric bimorph is linear with the excitation voltage. Compared with the existing demonstration experiments, the conversion relationship between mechanical energy and electrical energy are investigated in this new designed experiment, which is helpful to make participants understand deeply of the principle of piezoelectric effects.

Walton: From experimenter to great master

JIANG Yu-jing, LU Jian-long

College Physics. 2022, 41(8):  52.  doi:10.16854/j.cnki.1000-0712.210577

Abstract ( 362 )   PDF (859KB) ( 168 )  

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Relativity is Einstein^,s greatest scientific contribution to mankind, especially the popular mass-energy equation. However, physicists who proved Einstein^,s mass-energy equation by experiments were not known much until the Manhattan Project created the atomic bomb. In fact, as early as 1932, Walton from Ireland and Cockcroft from Britain successfully proved the equivalence of Einstein^,s mass-energy equation in the process of experiments of splitting atoms. Walton and Cockcroft shared the Hughes Medal in 1938 and the Nobel Prize in physics in 1951 for their great achievement of “disintegration of atomic nuclei by artificially accelerated atomic particles” in 1932. Comparing with Cockcroft^,s enthusiasm and extroversion, Walton was low-key, modest and introverted. His quiet personality perhaps have led many people to overlook his outstanding scientific achievements and social contributions. Taking the 90th anniversary of the verification of the mass-energy equation as an opportunity, this paper gives a detailed and comprehensive introduction to Walton who is a low-key but much-loved Irish physicist.

Exploration of human-computer interaction teaching mode based on the harmonic motions and its combination and decomposition by using Jupyter lab

WU Tao, LIU Yang, WANG Shi-fang

College Physics. 2022, 41(8):  59.  doi:10.16854/j.cnki.1000-0712.210400

Abstract ( 287 )   PDF (1134KB) ( 139 )  

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In this paper, the man-machine interactive and visualized teaching mode of the simple harmonic vibration in college physics textbook is comprehensively introduced based on the platform of Jupyter lab/notebook and the 3D animation Vpython. This teaching mode provides a new method to students for easily comprehending physics concepts and establishing physics images. In order to increase the students’ learning interest and training their computing thinking, it is also a good example for exploring the reform of new engineering teaching mode. The interactive visualization method and coding technology may be utilized and improved in other content module of college physics education.

Practice of multiple intergrated PAD class in university physics teaching

MA Ling, CHEN Xin, LIN Bai-tong, HAO Rui, GAO Yong-wei, ZHANG Yi-bing

College Physics. 2022, 41(8):  65.  doi:10.16854 /j.cnki.1000-0712. 220004

Abstract ( 299 )   PDF (1098KB) ( 292 )  

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Aiming at the problems existing in university physics teaching, such as single teaching organization and assessment form, students^, lack of learning awareness, and the low classroom efficiency, innovative practice of multi-integration teaching mode is necessary. PAD class has the following features: First, it advocates teachers^, incisive teaching, students^, self-learning and discussion, so as to cultivate students^, ability of independent thinking, communication and cooperation. Second, the ideological and political elements are incorporated to inspire students^, self-confidence and national pride; Third, demonstrative experiments is introduced to make students deeply understand the nature of physics; Forth, project-based teaching and create scientific research situation is carried out to realize students^, deep learning; Fifth, the process assessment is strengthened to form reasonable diversified evaluation of students; Finally, relying on the information platform, teaching resources are effectively integrated and the efficiency of teaching management are comprehensively improved. PAD class puts the teacher-directed and student-oriented concept into effect, which meets the need of cultivating new engineering talents with connotative development under the new engineering background.






Discussion on the two-body problem

LIN Hao-chen, MA Li

College Physics. 2022, 41(8):  71.  doi:10.16854/j.cnki.1000-0712.210499

Abstract ( 572 )   PDF (844KB) ( 295 )  

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Two-body problems are very common in physics, especially in collision and celestial body problems. When the perturbation force of the multi-body problem is far less than the interaction force between two bodies, it can be approximated as a two-body system. In this paper, koenig^,s theorem is derived from two perspectives of transformation of reference frame and conservation of energy, which leads to the two-body modification of the problem by reduced mass, and puts forward the idea of equivalent integration to deal with the problem, which simplifies the discussion of the two-body problem. At the same time, the degenerate ellipse time method is introduced to solve the time problem from relative rest to collision of two bodies under inverse square force. Finally, we discuss and improve the multi-solution method of the two-body problem, and use the conclusion of the two-body problem of the celestial system to compare the two-body problem with the two-point charge problem, so as to avoid the complicated integration in the book, and highlight the superiority of the equivalent integration treatment of the problem.

Numerical investigation on submergence time of Saxon bowl

ZHANG Ting-jun, SHI Xin-yu, WANG Xu-sheng

College Physics. 2022, 41(8):  76.  doi:10.16854/j.cnki.1000-0712.210515

Abstract ( 457 )   PDF (897KB) ( 154 )  

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Saxon bowl is a timing tool of the ancient Saxon. There is a hole in the center of its bottom and the bowl will sink after being placed on the water. We establish a model through Bernoulli equation and boundary layer theory, and then carry out numerical calculation to obtain submergence time, and compare it with experience. The results show that when the outer diameter of the bowl is more than 10 times of the bottom aperture, the model can well describe various experimental results, including the changes of submergence time with the aperture, mass of the bowl and liquid density. The model also reveals two special phenomena. First, with the increase of bowl mass, the submergence time tends to zero. Second, as liquid density exceeds density of the bowl, the bowl will not sink. The main advantages of the model are that it can accurately describe the experimental data and the speed correction term CD has great universality and insensitivity. The main limitation are its description of turbulence and an extreme situation.

Using Michelson interferometer to measure  the characteristic parameters of optical filter

GAO Chong-han, AN Wei, WANG Zheng, XU Ping

College Physics. 2022, 41(8):  81.  doi:10.16854/j.cnki.1000-0712.210611

Abstract ( 380 )   PDF (967KB) ( 194 )  

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Optical filter is an optical element that can select a certain wavelength range from white light, and is widely used in photography and detection systems. Its main parameters are central wavelength and bandwidth. In this paper, a Michelson interferometer is used to measure the characteristic parameters of narrow-band filter based on the Fourier transform principle. The measurement results are compared with the traditional diffraction grating method. It is found that the measurement done by Michelson interferometer does not need the calibration of the Mercury lamp and the results are more accurate than the traditional diffraction grating method. Moreover, the present method could improve students^, ability of solving practical problems by using multi-disciplinary knowledge comprehensively.