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    22 October 2022 Volume 41 Issue 10
      
    Some thoughts on teaching solid state physics Ⅲ:  the relaxation time approximation
    LIU Yi, YUAN Zhe
    College Physics. 2022, 41(10):  1.  doi:10.16854/j.cnki.1000-0712.220074
    Abstract ( 1005 )   PDF (803KB) ( 506 )  
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    The relaxation time approximation is an important formalism to deal with the transport phenomena in solid state physics. It is also a frequently applied method in the research of condensed matter physics. The physical background and advantages of the relaxation time approximation is usually missing in many solid-state physics textbooks. Here the mathematical expression is obtained by analyzing the physical process of electron collisions during transport. Then the formal solution of the non-equilibrium distribution function under relaxation time approximation is analytically solved. In this paper concise and logical contents for teaching the relaxation time approxi mation in solid state physics are established,which are helpful for students to fully and deeply understand the related physics and to apply the approximation in the research of condensed matter physics.

    Teaching practice of four elements for insight and idea in Electrodynamics
    HU Xiang-ming
    College Physics. 2022, 41(10):  4.  doi:10.16854 /j.cnki.1000-0712.220060
    Abstract ( 456 )   PDF (880KB) ( 272 )  
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    Morality and principle,insight and idea,ability and competence,knowledge and experience constitute four requisite qualities for a scientific talent. Of them,insight and idea mean capability to look far ahead and to make a foresight. In this article four elements are described to be inspired for insight and idea in the teaching practice of Electrodynamics. The first is to be good at giving an idea daringly and proving it carefully; the second is to be good at testing and verifying an idea experimentally; the third is to be good at discovering something new from a contradictory ; the forth is to be good at using mathematics for physical reasoning . The inspiration of these four elements is based on the historical facts in science. It depends on the great scientists as examples,it is blended with Maxwell equations’ understanding and applications,and it is aimed at the scientific view guidance to the students. The teaching practice of it,which has been carried out at national base for training talents for research and teaching in fundamental science (physics)at Central China Normal University,has demonstrated that it helps students promote their interest and perseverance for the Electrodynamics learning and enhance their confidence and potential for their future comprehensive development. 

    Asymmetric integral projection operators constructed by coordinate #br# and momentum representations and parity measurement#br#
    WANG Shuai, ZHANG Jian-dong, WANG Feng-fei, ZHU Xiao-qin
    College Physics. 2022, 41(10):  12.  doi:10.16854/j.cnki.1000-0712.210464
    Abstract ( 561 )   PDF (799KB) ( 216 )  
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    Quantum states together with operators provide the statistical description of any property of the system,which play important role in quantum theory. Based on coordinate and momentum quantum representations,a new kind of asymmetric integral projection operators is introduced,which is proved to be the Hermitian operator. By means of the technique of integration within an ordered product of operators,we obtain the normal ordering form of such Hermitian operator. In addition,it has been proved that such Herimtian operator corresponds to the parity measurement of the phase estimation in a MachZehnder interferometer .

    Relationship between thermodynamic probability  and molecular number of ideal gas
    LIU Zhi-guo, ZHANG Yao-hui, WANG Xian-jie, ZHANG Ling-li, HUANG Xi-qiang, WANG Xiao-ou, ZHANG Yu
    College Physics. 2022, 41(10):  15.  doi:10.16854/j.cnki.1000-0712.220008
    Abstract ( 850 )   PDF (763KB) ( 332 )  
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    Thermodynamic probability is an important concept in statistical physics, and relates to the Boltzmann entropy directly. In this paper, factors governing thermodynamic probability are analyzed, which may be neglected in calculation, i.e., the state of ideal gas imposes restrictions, and ensures the Boltzmann entropy an extensive quantity. The thermodynamic probability change of the following processes of ideal gas is calculated, i.e., adiabatic free expansion, isothermal expansion and varying molecular number under isothermal and isobaric conditions. 

    Numerical calculation of magnetic dipole electromagnetic field with its algebraic form and integral expression
    HONG De-cheng, WANG Hai-jun
    College Physics. 2022, 41(10):  18. 
    Abstract ( 429 )   PDF (814KB) ( 271 )  
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    In recent years, computational physics has attracted more and more attention in college physics education. In this paper, we derive the algebraic form and the integral expression of electromagnetic field excited by magnetic dipole source in uniform medium. The solution is solved by introducing Hertz potential based on Maxwell equations. Cubic spline fitting method and Gauss-Legendre numerical integration method are used to solve this numerical integral problem, and its numerical results are verified with the algebraic form. It also provides students an electrodynamics calculation case including both physical background and numerical calculation method.

    Formation mechanism and reappearance experiment of Fata Morgana phenomenon
    CHEN Jia-bin, XU Qiang, WANG Wei, ZHONG Ming, LU Jian-long
    College Physics. 2022, 41(10):  23. 
    Abstract ( 428 )   PDF (1078KB) ( 232 )  
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    Fata Morgana phenomenon is a beautiful and complex illusion due to the refraction and total reflection of light in a certain fluid. In this paper, the physical mechanism of Fata Morgana phenomenon is analyzed, and the imaging mechanism of single image extension, contraction, inverted and multiple image overlapping of Fata Morgana phenomenon are qualitatively analyzed. The Fata Morgana phenomenon is reproduced through experiments. Using the laser display light path, the ray trajectory equation in single-layer medium is deduced theoretically, the causes of various complex phenomena are analyzed and verified by experiments.

    Improvement of the experiment for measuring Young,s  modulus with optical lever method 
    ZHANG Li, RONG Zhen-yu, WANG Han-yu, JIANG Heng-jun, HAN Yu-jing, CHEN Xiao-yi
    College Physics. 2022, 41(10):  29. 
    Abstract ( 1386 )   PDF (992KB) ( 558 )  
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    In traditional optical lever method for measuring Young,s modulus, it needs to measure the distance between the optical lever plane mirror and the ruler. It is inconvenient to measure the larger distance between the optical lever plane mirror and the ruler in experimental operation. In this paper, a translation stage with reading device is installed under the ruler of the traditional optical lever instrument. It makes the experimental measurement more convenient by obtaining the change of the distance between the optical lever plane mirror and the ruler via the reading device of the translation stage. Moreover, the random error can be reduced through multiple measurements.


    Numerical simulation of the interaction between circular  polarized lights and graphene metasurfaces
    HU Li, XI Feng, DAI Hong-xia
    College Physics. 2022, 41(10):  33. 
    Abstract ( 249 )   PDF (902KB) ( 340 )  
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    Based on the finite element method, the interaction between cirular polarized lights and graphene metasurfaces is simulated, which shows the properities of the far-field and near-field responses of graphene metasurfaces. Results show that the plasmonic resonances are stimulated by circular polarized lights at the mid-infrared region. The absorption spectra are independent with the polarized direction of incident lights, which results in zero far-field chiral responses. However, the surface charge distributions, the local electric fields and the chiral near-fields are closely related to the polarized direction of incident lights. Through numerical simulation, the knowledges of cirular polarized lights and electromagnetism can be shown vividly, which should deepen students’ understanding and stimulate students’ creative consciousness.

    Application of approaching saturation law in the study  of magnetic properties of nano-permanent magnetic materials
    LV Qing-rong, HUANG Jing-wen, FENG Shuang-jiu
    College Physics. 2022, 41(10):  37.  doi:10.16854 /j.cnki.1000-0712.220019
    Abstract ( 434 )   PDF (864KB) ( 177 )  
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    The magnetization curves and hysteresis loops of nano-cobalt ferrite samples are measured at temperatures of 5 K and 300 K. It is found that the material has large coercivity at low temperature of 5 K, and the coercivity decreases with the increase of temperature. The saturation magnetization and magnetocrystalline anisotropy constant of the material are calculated using the approaching saturation law. As the temperature increases, the thermal disturbance energy increases and the saturation magnetization decreases. The calculated results are consistent with the theoretical analysis. The magnetocrystalline anisotropy is the main factor affecting the coercive force. The calculation results show that the material has large magnetocrystalline anisotropy constant at low temperature of 5 K. With the increase of temperature, the magnetocrystalline anisotropy constant decreases rapidly, which is consistent with the trend of coercive force with temperature.

    The second philosophy: the decisive factor that help Chen Ning Yang to win in scientific research
    HOU Yu-de
    College Physics. 2022, 41(10):  40.  doi:10.16854 /j.cnki.1000-0712.220005
    Abstract ( 493 )   PDF (829KB) ( 310 )  
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    Chen Ning Yang believes that in his scientific period, “the first philosophy” (that is, the philosophy of philosophers) can not provide effective assistance to the research work of theoretical physicists anymore; by contrast , Chen Ning Yang pointed out that “the second philosophy” of theoretical physicists’ has a key decisive role in their professional research work. Research shows that Chen Ning Yang’s thoughts have gone through three stages: style, taste, and “the second philosophy”, in which it gradually became more clearer and more accurate. Discriminating Chen Ning Yangs statements on different occasions, from philosophical perspective, could find out that Chen Ning Yangs “the second philosophy” is a scientific “empirical theory” based on physical phenomena; it belongs to the category of validation theory philosophy which based on induction. Chen Ning Yang emphasized that “the second philosophy” is not method, but it has the function of choosing valuable research topics and choosing corresponding research methods; this function often works in the subconscious state by intuition, and is source for creation of theoretical physicists. “The second philosophy” and the “world of knowledge” are relatively independent, and also have positive interactions. The two cannot replace each other, a reasonable reserve of knowledge is an important guarantee for “the second philosophy” to play its role.

    Middle-level practice to enhance college students, problem-solving ability 
    LI Zu-bin
    College Physics. 2022, 41(10):  47.  doi:10.16854/j.cnki.1000-0712.210646
    Abstract ( 368 )   PDF (787KB) ( 151 )  
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    Training students, problem-solving ability is an important part of university education. Between the basic level exercises for the purpose of mastering knowledge and the high-level ability for training requiring innovative ability, the intermediate level practice are set up in the form of post-class thinking problems for training students to use learned knowledge to solve some open or practical problems. The training of students, problem-solving ability is also the requirement of ideological and political education in the curriculum. At the same time, ideological and political elements can also be integrated into the problems to cultivate students, scientific spirit of exploration and to pursuit new knowledge.

    Exploration and practice of online and offline blended teaching of college physics
    QI muge
    College Physics. 2022, 41(10):  51.  doi:10.16854/j.cnki.1000-0712.220099
    Abstract ( 496 )   PDF (1007KB) ( 290 )  
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    In the post-epidemic era, online and offline blended teaching is gradually becoming the main trend of course teaching. Blended teaching can be divided according to content, some content is placed online, and some content is placed offline; it can also be divided according to space, some students study online and some students study offline; they can also be divided by function, and the lectures are offline, and the assignments, tests, and answers are online. This article takes the teaching of the college physics course as an example to illustrate the complete teaching process of online and offline hybrid teaching in detail. Compared with traditional teaching, online and offline hybrid teaching has obvious advantages in dealing with the epidemic, assessment and evaluation, and teaching effect.

    Dynamics of a rigid sphere on a rotating annular groove
    LEI Jia-rui, HAN Run-ze, WANG Ke-ren, HUANG Min, ZHAO Yun-he, MA Yu-han
    College Physics. 2022, 41(10):  55.  doi:10.16854/j.cnki.1000-0712.210605
    Abstract ( 583 )   PDF (1106KB) ( 373 )  
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    In this paper, the dynamics and trajectory of a rigid sphere in an annular groove rotating around a vertical axis is studied. The rotation and revolution of the sphere are coupled with each other through friction. Theoretically, the balance position of the sphere which monotonically increases with the rotating speed of the annular groove is obtained. And the damped oscillation of the sphere is solved numerically. In addition, an experimental setup is built with the help of 3D printing, and a method is proposed for measuring friction coefficient between the arc surface and the object thereon. The theoretical predictions are quantitatively verified by the experimental results. 

    The internal structure of the rotational polytropes
    LUO Xin-rui, YU Cong
    College Physics. 2022, 41(10):  59.  doi:10.16854 /j.cnki.1000-0712.210402
    Abstract ( 333 )   PDF (1053KB) ( 198 )  
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    Polytrope is often used to describe the internal structure of gaseous stars. For a stationary polytropes, the Lane-Emden equation can be obtained bycombing the hydrostatic equilibrium equation with the polytropic equation, and the internal structure of the star can be determined approximately by solving the equation. But for the more general cases, the star is in rotation. Hence the influence of rotation on the outer boundary and inner structure of the polytrope model is particularly important. This paper firstly substitutes the rotation into the hydrostatic equilibrium equation and combines the polytropic equation to obtain a differential equation that can describe the internal structure of the star in the case of rotation, and then considers the case of slow rotation, and uses the method of perturbation expansion and separation of variables to obtain a approximated solution. Finally, the outer boundary, internal density distribution and the relationship of mass and radius of the rotation polytrope are discussed through the approximated solution.

    Quantitative analysis and simulation of fata morgana
    YU Xiao-fei, ZHOU Wei, WANG Dian-sheng, WANG Yu-dou, LI Dai-lin
    College Physics. 2022, 41(10):  67.  doi:10.16854 /j.cnki.1000-0712.210321
    Abstract ( 394 )   PDF (1076KB) ( 142 )  
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     Fata Morgana phenomena are usually presented in the vertical direction with more than three mirages at the same time, which are upright or inverted, alternating tensed and compressed, and distorted. In this paper, the complex optical phenomenon is reproduced by physical experiment and the variation of mirage with observation distance is explored. Then the variation law of mirage is analyzed quantitatively by numerical simulation. The results show that the number, position and shape of the mirage vary with the distance of observer, gradient of refractive index and thickness of the medium. The compression ratio and initial distance of the inverted mirage are positively and negatively correlating with the gradient of the medium respectively, while the distance between upright mirage and inverted mirage is negatively correlating with the thickness of the medium.

    Study on the movement of the homopolar placed on the aluminum foil
    WANG Rong-chao, XV Xiao-wen, LIU Xin-di, DONG Qi
    College Physics. 2022, 41(10):  75.  doi:10.16854/j.cnki.1000-0712.210556
    Abstract ( 353 )   PDF (916KB) ( 149 )  
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    On the basis of existing experiments, we improve the experimental device and analyzed the influence on magnets that was exerted by the current flow direction and the temperature. Meanwhile, we have observed the cylindrical battery and the homo-polar roller which was composed by the button magnets (permanent magnets) absorbed at both ends. It is found that when the homo-pole roller is placed on the aluminum foil, the magnets with same or different radii at both ends lead to disparate movement phenomena, respectively. We analyze the roller’s moving course on the foundation of simplified dynamics theory and obtained the relationship between the displacement and time with the same radius as well as the relationship between the magnet radius and the magnet moving radius with different radius by combining the simulation and experiment. 

    A review of dark matter and modified Newtonian dynamics
    ZHENG Xue-yao, KANG Xian-wei, ZHANG Feng-shou
    College Physics. 2022, 41(10):  80.  doi:10.16854 /j.cnki.1000-0712.220041
    Abstract ( 530 )   PDF (901KB) ( 276 )  
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    The current literature compares the dark matter model and the modified Newtonian dynamics theory, and respectively explains how they solve the existing problems of astronomical observations. Furthermore, we introduce the development of dark matter model, list the main important evidence and prospective candidates for dark matter, and summarize the existing methods to detect dark matter and their limitations. In addition, this literature introduces the development of the modified Newtonian dynamics theory, and summarizes the problems to be solved and the significant current progress. Finally, we compare the advantages and limitations of these two theories, and discuss the significance of this research and the future research direction.