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    17 June 2024 Volume 43 Issue 04
      
    Applications of the time-averaging method to physics problems
    TIAN Hong, WANG Xue
    College Physics. 2024, 43(04):  1.  doi:10.16854/j.cnki.1000-0712.230293
    Abstract ( 196 )   PDF (724KB) ( 228 )  
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    The time-averaging method is a mathematical technique employed to approximate certain rapidly fluctuating physical quantities by utilizing their average values over a specific time interval. This method is particularly relevant when the response speed of a physical system is considerably lower than the rate at which external excitation changes occur. Serving as a valuable model simplification tool, the time-averaging method enables the rapid extraction of pertinent information from time-varying signals, including those with oscillatory or noisy characteristics, thereby fostering a deeper comprehension of underlying physical processes. This paper employs the time-averaging characteristics of the sine function as a mathematical foundation and proceeds to provide a succinct exposition and analysis of the diverse applications of the time-averaging method in various branches of physics, such as mechanics, optics, and magnetism.

    Application of analogical thinking in constructing light transmission theory of temporal multilayer media
    WU Hong-wei, CHEN Xue, SHENG Zong-qiang
    College Physics. 2024, 43(04):  5.  doi:10.16854/j.cnki.1000-0712.230133
    Abstract ( 114 )   PDF (819KB) ( 93 )  
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    The multilayer media theory and the transmission matrix method are introduced in detail in Principles of Optics, which is a classic textbook for graduate students majoring in optics and physics. Due to the duality of time and space, in this paper, the propagated characteristics of light in the temporal multilayer media whose material parameters change with time is mainly expounded and the form of transmission matrix in the temporal multilayer media is deduced. Finally, by comparing the transmitted and reflected coefficients of temporally periodic multilayer media and spatially periodic multilayer media, the connection and difference between them are deeply discussed. 

    A method for constructing non-polynomial QES potential
    HU Fu-wang, XIAO Bei
    College Physics. 2024, 43(04):  10.  doi:10.16854/j.cnki.1000-0712.230106
    Abstract ( 83 )   PDF (756KB) ( 83 )  
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     There are many approachs to construct quasi-exact solvable problems, such as supersymmetric method, Darboux method, Lie algebra method, etc., but the quasi-exact solvable problems constructed by these methods are often polynomial wave functions. Starting from a class of double well with parametric variation, we study the properties related to the parameters, and find a method to construct QES potential. The QES potential constructed by this method has Lie algebraic structure, but the form of the wave function is non-polynomial.

    double-parameter perturbation method
    XU Ning, WU Feng
    College Physics. 2024, 43(04):  15.  doi:10.16854/j.cnki.1000-0712.230107
    Abstract ( 101 )   PDF (803KB) ( 80 )  
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    By using the double-parameter perturbation method combined with a double-fold perturbation scheme, the energy levels for the low-lying excited states 1s2ns (n=3,4,5) of lithium-like atoms are calculated. The calculated results are in well agreement with experiment within a relative error of 0.8%. It is found that the electron can be regarded as moving in a circular orbit, corresponding to the assumption of steady state in Bohr theory. Moreover, it is shown that with the increase of the excited state of atom, the effective charge of inner electron remains largely the same, but the effective charge of the outer electron of the atom decreases. These findings would deepen our understanding of the electron related effects in atoms.

    Rotation inertia center of rigid body
    College Physics. 2024, 43(04):  19.  doi:10.16854/j.cnki.1000-0712.230248
    Abstract ( 180 )   PDF (693KB) ( 133 )  
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    The moment of inertia is the measure of the rotational inertia of the rigid body, and the rotational inertia center is the special rotational center of the rigid body. The inertia tensor to the rotation center is a secondorder spherical tensor. The moment of inertia of a rigid body is equal to any axis passing through the rotational inertia center, and any axis passing through the rotation center is the principal axis of inertia. The theorem for the rotation inertia center is proposed and proved, namely,  when the three principal moments of inertia to the center of mass are equal, the center of mass is the only rotation center; When only two smaller principal moments of inertia are equal, the rigid body has only two rotation centers, both on the principal axis of larger principal moment and symmetrically distributed with respect to the center of mass, and the distance from the two rotation centers to the center of mass is equal to the square root of the ratio of the difference between the larger and smaller principal moment of inertia to the mass of the rigid body; When the three principal moments of inertia are not equal to each other or only two larger of them are equal, there is no rotation inertia center.
    Study on exact classical and quantum dynamics of two coupled driven harmonic oscillators
    CHEN Kang-kang, LI Hai-feng, OU Zhi-min, ZHANG Kai-feng
    College Physics. 2024, 43(04):  22.  doi:10.16854/j.cnki.1000-0712.230193
    Abstract ( 258 )   PDF (746KB) ( 200 )  
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    The harmonic oscillator model, which can be analytically solved, takes an important part in physics and is a powerful theoretical model for describing many physical processes. However, the research on driven harmonic oscillator is rarely involved. In this paper, we study the exact classical and quantum dynamics of two coupled harmonic oscillators in the driving external fields. In the framework of classical mechanics, the exact energy values of the time-dependent external fields acting on two coupled harmonic oscillator systems are obtained by virtue of the Hamiltonian canonical equations. If the driven fields are constant, the energy eigenvalues and eigenstates of the system in quantum mechanics are attained. In consideration of the time-dependent driven fields, the expected energy values and wave function of quantum system are derived using operator algebra methods. Because the microscopic particles have wave-particle duality within the framework of quantum mechanics, there are obvious differences between the classical and quantum dynamics for the system consisted of the two coupled harmonic oscillators in the external driving fields.

    Solving Feynman's traveling field problem using retarded potential
    LI Zhao-yu
    College Physics. 2024, 43(04):  26.  doi:10.16854/j.cnki.1000-0712.230227
    Abstract ( 121 )   PDF (719KB) ( 95 )  
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     In this paper, we use the retarded potential to solve the traveling field problem proposed by Feynman in his lectures on physics. Compared with general electromagnetic radiation problems, the retarded potential solution has the following characteristics in this particular problem: (1) the retarded potential is simple to integrate, and an exact analytical solution can be obtained; (2) the physical idea is clear, and the physical concept of "electromagnetic action propagates with finite speed" contained in the retarded potential formula is fully demonstrated in the solving process.

    Discussion on the paper titled “questions and reflections on Rabi’s signal theory in College Physics”#br#
    ZHANG Zhi-ming
    College Physics. 2024, 43(04):  29.  doi:10.16854/j.cnki.1000-0712.230214
    Abstract ( 89 )   PDF (674KB) ( 91 )  
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    The problem in the paper titled “questions and reflections on Rabi’s signal theory” in College Physics is rediscussed. Our theoretical deduction is more concise, and our physics explanation is clearer. We emphasize once more that the quantum states are described  by probability amplitudes, not by probabilities. The states with a same probability can have different probability amplitudes, so they are different states.

    Discrimination of theterminology of laws in university physics#br#
    ZHANG Yong, ZHANG Nai-bo, WU Pei-weng, HOU Ji-xuan
    College Physics. 2024, 43(04):  31.  doi:10.16854/j.cnki.1000-0712.230304
    Abstract ( 147 )   PDF (799KB) ( 141 )  
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    Taking physical laws in university physics textbooks as an example, the rules of terminology of physical laws, theorems, principles, postulates, rules and models, as well as their difference and connection are studied in this paper. Based on this work, the different terminology of the same rule in classical textbook of China and abroad can be not only elucidated but also understood and discriminated these physical rules with the help of comparison analysis of their formation background, creation process, logical method, theory hierarchy, time of verification, property of description, relationship of affiliation and degree of convenience. The difference of terminology of some physical rules lies in their different connotation and logical sequence in instruction in domestic and foreign textbooks. Findings of this research are helpful in the teaching aiming at subject literacy improvement as well as in the building of knowledge map.


    Theoretical derivation of the physical analytical model of short-channel negative capacitance gate-all-around field effect transistor
    College Physics. 2024, 43(04):  36.  doi:10.16854/j.cnki.1000-0712.230335
    Abstract ( 115 )   PDF (1050KB) ( 135 )  
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     EDA design software of Gate-All-Around Field-Effect Transistor (GAAFET) is one of the key technologies in chip industry in our country, which has been paid high attention by science and industry. In this paper, the physical analytical model of the traditional short-channel GAAFET is derived by reasonable approximation, and then the physical analytical model of the negative capacitance GAAFET is derived by adding ferroelectric layer. The derivation of the physical model is helpful to deepen students understanding of the working principle of GAAFET, stimulate students learning interest and improve their research ability.
    Introducing first-principles calculations into the teaching of college physics simulation experiment#br#
    ZHOU Meng1, TAO Ying-qi1, CHENG Cai2
    College Physics. 2024, 43(04):  40.  doi:10.16854/j.cnki.1000-0712.230058
    Abstract ( 120 )   PDF (816KB) ( 377 )  
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    This article explores the use of first-principles calculations in university physics simulation experiments. That is a typical material in conductor and semiconductor as well as insulator materials is selected to analyze its optimal structure at zero temperature and zero pressure. Then, through the analysis of band structure, the microscopic cause of electrical conductivity is found. In this paper, the introduction of computational physics into college physics simulation experiments can not only guide students to explore the microscopic structure of matter, but also broaden their views through the understanding of high and new technologies, and serve for the cultivation of innovative talents.

    Method for measuring Young’s modulus by replacing optical levers with optical interference and diffraction devices
    WANG Guo-you, FAN Qin, ZI Xiong, ZHU Wen-yi, CHEN Guang-wei, CHEN lang
    College Physics. 2024, 43(04):  44.  doi:10.16854/j.cnki.1000-0712.230126
    Abstract ( 172 )   PDF (1146KB) ( 214 )  
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    A Young’s modulus experimental instrument is designed based on the principles of light interference and single-slit diffraction. According to the change rule of fringes of light interference and diffraction, the tiny length change of metal wire under tension can be measured, and then the high precision measurement of Young’s modulus of metal wire is realized. To satisfy the experimental conditions for interference of light, a pneumatic tension adjusting device is designed to replace weights, in which the shaking problem of the instrument is solved and the stepless adjustment of tension change and the reading of tension directly from the electronic scale are realized. The instrument also make a simple traditional mechanical experiment change into a comprehensive experiment combining mechanics and optics for measuring Young’s modulus, which enriches the experimental content, broadens the students’ vision, and improves their comprehensive ability to analyze and solve problems.

    Analysis and discussion on the resonator adjustment in laser gyro experiment
    ZHANG Yi, TAN Zhong-qi, YUAN Jie, LIANG Yong-hui, JIANG Qi-yuan, SUN Bing-feng
    College Physics. 2024, 43(04):  49.  doi:10.16854/j.cnki.1000-0712.230169
    Abstract ( 120 )   PDF (879KB) ( 110 )  
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     Under the condition of non-paraxial approximation, a formula of the relationship between the cavity size, mirror curvature, deflection angle and the space position of self-reproduction resonant laser in the laser gyro experiment is derived by using geometric optics theory. The difference between the formula and the matrix optical results under the usual paraxial approximation is compared. The effect of adjusting the mirror deflection angle on the effective cavity length, optical path area, gyro scale factor and laser output position is discussed, which has guiding significance for the adjustment of resonator in laser gyro experiment.

    A study on the free falling motion of raindrops with a diameter of 5 mm in still air at 20 ℃#br#
    SHAO Yun
    College Physics. 2024, 43(04):  56.  doi:10.16854/j.cnki.1000-0712.230185
    Abstract ( 279 )   PDF (791KB) ( 146 )  
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    The article adopts the spherical raindrop model and uses the strict expression of the air resistance coefficient CD, namely the Wallis formula, to calculate the v~t image of a raindrop with a diameter of 5 mm when it freely falls from rest in still air at 20 ℃. The article also solves the analytical and universal v(t) function under the approximation of CD being uniformly taken as 0.44, and produces the corresponding v~t image. The results show that these two v~t curves almost completely coincide, indicating that the approximate treatment is completely appropriate. The article explains the reason for this and points out the reason for the limit rate measured in the experiment is 2.00 m/s lower than the theoretical value under the spherical raindrop model is the actual raindrop shape presents a Hamburg shape, and its actual air resistance coefficient is calculated to be about 0.52. We believe that the spherical raindrop model is generally practical.

    On the rationality of the uniform motion treatment in the centrifugal separation theory
    GUO Zhen-dong
    College Physics. 2024, 43(04):  61.  doi:10.16854/j.cnki.1000-0712.230191
    Abstract ( 265 )   PDF (748KB) ( 137 )  
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    The centrifugal technique is an experimental technique, which separates particulate matter according to the difference of the sedimentation coefficient by centrifugal force. However, numerous approximate treatments exist in the centrifugal separation theory, such as ignoring Coriolis force, treating the centrifugal process of particulate matter as a uniform motion. In this research, a rigorous kinetic analysis for the centrifugal process of particulate matter by differential centrifugation method and sedimentation velocity method is carried out according to the basic principles of Newtonian mechanics. Combining with numerical calculation of the relevant parameters of bovine serum albumin (BSA), this research focuses on the rationality of the uniform motion treatment.

    Theoretical research and visualization of the yarn winding problem
    CHEN Miao, GUO Qin
    College Physics. 2024, 43(04):  65.  doi:10.16854/j.cnki.1000-0712.230114
    Abstract ( 105 )   PDF (814KB) ( 83 )  
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    The yarn winding process is an important part of the textile process and has a wide range of applications in the light industry and handicraft industry. In this paper, the yarn winding process is simplified as a string vibration process. The Fourier series method and the impulse theorem method are used to solve the fixed solution problem of the yarn winding problem, and then the vibration solution of the winding air loop is obtained. From the perspective of energy, the reason why the winding air loop is a standing wave is explained. With the aid of mathematical software, the motion state of the winding air loop is visualized. The shape of the winding air loop under different vibration wave velocities and unwinding angular velocities is investigated, and some interesting conclusions are obtained.

    Experimental exploration of Boycott effect and modification of PNK theory
    FANG Jun, HAN Lu, ZHONG Ming
    College Physics. 2024, 43(04):  69. 
    Abstract ( 125 )   PDF (887KB) ( 160 )  
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    When a test tube is tilted, the settling rate of suspended particles is faster than that when the test tube is vertical. This is known as Boycott effect which has been subject to various theoretical explanations. In this study, Boycott effect is experimentally investigated with particle size, test tube tilt angle and particle density as variables. Liang-kai Huang′s fuzzy threshold method is used to accurately determine the settling rate from images obtained during experiments. The Krieger-Dougherty model is used to modify the traditional PNK theory of viscosity coefficient in the theoretical analysis. The results from the experiment are in good agreement with the modified theory.

    Sound intensity measurement and precision analysis based on rayleigh disk
    XING Yu-man, WU Jia-sheng, HAN Lu, ZHONG Ming
    College Physics. 2024, 43(04):  75.  doi:10.16854/j.cnki.1000-0712.230284
    Abstract ( 119 )   PDF (844KB) ( 109 )  
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     When a disc is suspended vertically by thin lines in sound field, this device can be rotated around an axis to measure the intensity of sound and a simple Rayleigh disk. In this paper, this phenomenon is theoretically analyzed and modified from field theory point of view. The relationship between sound intensity and rotation angle of disk is analyzed. The accuracy of the device is studied deeply through calibration experiments. The influence of relevant parameters on the accuracy of Rayleigh disk is explained. The optimal parameter for designing the Rayleigh disk device is determined.

    The aesthetics for low-dimensional topological insulators  in condensed matter physics
    LI Zheng-he1, 2 , TANG Zi-kang2
    College Physics. 2024, 43(04):  81.  doi:10.16854/j.cnki.1000-07121.230243
    Abstract ( 158 )   PDF (832KB) ( 302 )  
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    Low-dimensional topological insulators are the frontier of condensed matter physics in semiconductor power devices and solid materials. Physicists combine the theory of condensed matter physics and topology to analyse and explore the solid state structure and properties of electron spin in low-dimensional mercury telluride (HgTe). The quantum spin Hall effect and the topological quantum doublet are two significant physical theories of low-dimensional topological insulators,which play a fundamental role in predicting and discovering the material configuration and energy band structure of topological insulators. A strong field physics is used to prove them experimently. In conclusion,the low-dimensional topological insulators are the frontier theory and material application of condensed matter physics,which is incorporated with the theory of mathematical topology and thus represent the aesthetics of condensed matter.