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Condition of half-wave loss when light is emitted from optically  denser medium to optically thinner medium QIU Hui-bin, WU Jun-jie, XIAO Dong-hua, HU Tian-yi, ZHONG Cheng-jie, LI Xiao-bin College Physics    2022, 41 (6): 40-.   DOI: 10.16854/j.cnki.1000-0712.210465 Abstract （3836）      PDF（pc） （475KB）（842）       Knowledge map    Save Through detailed derivation, graph presentation and discussion of the ratio relationship between the amplitude of the reflected wave and that of the incident wave, this article gives the detailed distribution map of phase difference between the reflected light and the incident light in the refractive index-incident angle space. At the same time, various conditions for the occurrence of half-wave loss are specified, including the half-wave loss of the reflected light when the light is emitted from the optically denser medium to the optically thinner medium. Here we show that when the light beam is shot from the optically denser medium to the optically thinner medium, the reflected wave may also occur half-wave loss; when the light beam is shot from the optically thinner medium to the optically denser medium, the reflected wave does not necessarily occur a half-wave loss. Our work clarifies and supplements some unclear conclusions in existing textbooks. Related Articles | Metrics | Comments（0）

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Application of tensor analysis in deriving geometric equations and equilibrium differential equations of elasticity in cylindrical coordinates and spherical coordinates ZHOU Zheng-feng College Physics    2022, 41 (11): 4-.   DOI: 10.16854 /j.cnki.1000-0712.220043 Abstract （2155）      PDF（pc） （226KB）（954）       Knowledge map    Save First, using the relations of the unit vectors between orthogonal curvilinear coordinates and Cartesian coordinates, and the invariability of the unit vectors in Cartesian coordinates, the gradient operator in both coordinates, and the partial derivative of the unit vectors to the coordinates are derived from the perspective of the transformation of the unit vectors. Then, using the fundamentals of the theorems of tensor field, the gradient of displacement vector and the divergence of stress tensor are derived by derivation. Last, the geometric equations of strain and the differential equations of equilibrium are derived in details in cylindrical coordinates and spherical coordinates from their forms expressed by tensor. Related Articles | Metrics | Comments（0）

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On the mathematical fundations of quantum mechanics YANG Shi-jie College Physics    2022, 41 (9): 4-.   DOI: 10.16854/j.cnki.1000-0712.210619 Abstract （1406）      PDF（pc） （2439KB）（1040）       Knowledge map    Save In this paper we present a comprehensive description of the mathematical foundations of quantum mechanics. The relevant topics include linear inner product, the completeness of Hilbert space, the functional space and continuous bases representations. We also discuss the self-adjoint operator, the eigen-value problem of the Sturm-Liouville system and the natural boundary conditions. We employ quantum problems as examples to discuss natural boundary condition under the non-regular singularity cases. These conditions are not externally applied but contain in the Schrdinger equation implicitly. Related Articles | Metrics | Comments（0）

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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 （1378）      PDF（pc） （992KB）（550）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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“Measure and object to reason, deliberate thinking and earnest action”— teaching  reform, innovation and practice of mathematics and physics method course ZHU Jun, LI Lu, LI Zhi-jian, MA Jie College Physics    2022, 41 (5): 41-.   DOI: 10.16854/j.cnki.1000-0712.210431 Abstract （1176）      PDF（pc） （292KB）（374）       Knowledge map    Save  The team of mathematics and physics method course in Shanxi university tried to reform and innovate all aspects of teaching. Teaching idea was innovated to achieve the goal of cultivating innovative and top physics talents. The teaching content was improved to reflect the function of connecting the preceding to the following and reorganized to meet the great demand of national research on quantum science and technology. The teaching mode was innovated to realize the student-centered teaching and the mutual integration of mathematics and physics. Objective and effective teaching evaluation ensured the teaching quality and improved teaching effect. Through ideological and political education, ‘spring breeze and rain, moisten things silently’ was realized. Related Articles | Metrics | Comments（0）

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Effect of sample stage height on the determination of lattice constants in XRD experiments WANG Hong-de, SUN Ying, YUAN Xiu-liang, AN Shi-hai College Physics    2022, 41 (9): 28-.   DOI: 10.16854/j.cnki.1000-0712.220064 Abstract （1123）      PDF（pc） （440KB）（352）       Knowledge map    Save X－ray diffraction ( XRD) is an important tool for analyzing the structure of substances and has been paid more and more attention in the teaching of physics － related majors． In this paper，the measurement errors caused by the variation of the sample stage height Δz are systematically analyzed． It is found that the sample stage height shift Δz causes a significant deviation in the diffraction peak position Δ2θ，which in turn causes a deviation in the calculation of the crystal interplanar spacing d and the lattice constant a． The results of the data fitting show that the deviation of Δd /d and the deviation of Δa /a for Si are approximately linear with Δz． Combined with the Bragg－Brentano diffraction geometry，we have theoretically analyzed the above experimental results． This work pro-vides a theoretical basis for the accurate determination of lattice constants in XRD experiments，and will also pro-vide an important reference for the development of related teaching work． Related Articles | Metrics | Comments（0）

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Strict proof of the commutation relations between orbital angular  momentum operator and vector operator as well as scalar operator QIN Xu-ming, KANG Dong-biao, HAO Hong-jun, ZHAO Dong-qiu, ZHANG Xi-wei College Physics    2022, 41 (12): 12-.   DOI: 10.16854/j.cnki.1000-0712.220022 Abstract （1111）      PDF（pc） （275KB）（728）       Knowledge map    Save Using the transformation characteristics of vector operator and scalar operator when space is rotated, this paper strictly proves the commutation relations between orbital angular momentum operator and vector operator as well as scalar operator, and constructs several specific scalar operators and vector operators to verify the commutation relations. Finally, the definitions of vector operator and scalar operator are discussed.  Related Articles | Metrics | Comments（0）

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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 （1066）      PDF（pc） （839KB）（258）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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Research on the coupled vibrations of Wilberforce pendulum DENG Xin-Yu, ZHANG Tian-YU, LU Jian-Long, ZHONG Ming, WANG Wei College Physics    2022, 41 (9): 43-.   DOI: 10.16854/j.cnki.1000-0712.220106 Abstract （1024）      PDF（pc） （907KB）（464）       Knowledge map    Save  Wilberforce pendulum is composed of a vertical spiral string and a pendulum bob fixed on the bottom of the string, it can vibrate vertically and rotate back and forth horizontally. In this paper, the reason why the amplitude of vertical oscillation and horizontal oscillation changes periodical is analyzed experimentally from the perspective of mechanics, and the motion of vertical oscillation and horizontal oscillation of Wilberforce pendulum from the perspective of analytical mechanics. The factors affecting the coupled motion state of Wilberforce pendulum are analyzed, and the experiment is used to study the influence of moment of inertia of Wilberforce pendulum on the coupled motion state. Wilberforce pendulum undergoes three motion states with the increase of moment of inertia: strong coupling, weak coupling and approximate decoupling. control variates are used to study the influence of the initial elongation of the string on the motion of Wilberforce pendulum. The results are in good agreement with the theoretical analysis. Related Articles | Metrics | Comments（0）

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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 （1002）      PDF（pc） （803KB）（505）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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Solution and visualization of wave functions in two-dimensional and  three-dimensional infinite deep annular potential wells WANG Yu-feng, FU Ke, WANG Yue-chao, SUI Lin-hong, JIANG Meng-yuan, FAN Ya-xi, LI Xi-bin College Physics    2023, 42 (1): 55-.   DOI: 10.16854/j.cnki.1000-0712.220299 Abstract （988）      PDF（pc） （313KB）（443）       Knowledge map    Save The Schrodinger equation of two-dimensional and three-dimensional infinite deep annular potential wells is solved by the method of separating variables. The eigenvalue of the radial wave function is determined by the zero point of the cross product combination of the Bessel function. For the three-dimensional case, the analyticalsolution of the ground state wave function can be obtained. For the excited state wave function, the radial probability density distribution is given by numerical method. For the two-dimensional infinite deep annular potential well, the radial probability density distributions of ground state and excited state are given by numerical method. Related Articles | Metrics | Comments（0）

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Several mean-value relations of a moving mass point  on elliptic trajectory under inverse squared centric force ZHOU Guo-quan, TANG Yu-xuan, QI Ning College Physics    2023, 42 (8): 6-.   DOI: 10.16854/j.cnki.10000712.220359 Abstract （928）      PDF（pc） （498KB）（988）       Knowledge map    Save  Based on Kepler's three laws, and the conservation laws of mechanic energy and angular moment about a mass point moving on an elliptic trajectory under an inverse-squared centric force, the mean values within a period of some typical physical quantity (polar radiurs，speed, angular speed, angular momentum, rotation inertia, kinetical energy，potential energy，and so on) ，are calculated and several interesting and useful mean-value relations are found and proved. A unique mean-value point on the path of the mass point is emphasized. The Virial theorem is direct proved by means of these calculated mean values. The physical meanings, and teaching reference significance of these findings are also emphasized. Related Articles | Metrics | Comments（0）

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Application of COMSOL simulation to acoustic resonant tube experiment LI Chun-yi, HU An-qi, ZHANG Ge-ge, BAI Zai-qiao, YU Xiao-chong College Physics    2022, 41 (11): 58-.   DOI: 10.16854/j.cnki.1000-0712.220159 Abstract （911）      PDF（pc） （626KB）（228）       Knowledge map    Save In this paper, COMSOL Multiphysics simulation is applied to acoustic resonant tube experiment. First the sound pressure distribution in the vicinity of tube end is calculated and the departure from the picture given by one-dimensional wave appxoimation is visulized. Then, the shift of resonant frequency is investigated due to the existence of sound detector (microphone). The result shows that the shift, which may be positive as well as negative,depends on the size and position of sound detactor. Finally, the resonant frequency of a tube with partly closed end is calculated and find that the numerical results agree with the mearsured values quite well. The stduy shows that numerical simulations can be applied to undergraduate physics laboratory to help students achieving a better understanding of experiments and endow them with a powerful tool to tackle practical problems. Related Articles | Metrics | Comments（0）

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COMSOL simulation of ferrite microwave circulator CAO Xiao, BAI Cui-qin College Physics    2022, 41 (9): 63-.   DOI: 10.16854/j.cnki.1000-0712.220035 Abstract （895）      PDF（pc） （600KB）（300）       Knowledge map    Save The circulator is a commonly used element in the microwave system, which is capable of selecting the directional propagation of microwaves. Since the microwave element is different from a low frequency centralized parameter element, the students are not easy to form a clear physical image. In this paper, the model of ferrite circulator is established by using COMSOL software. The influence of geometric parameters on the directional guided wave performance of circulator is quantitatively studied by using scattering matrix element (S parameter), and the corresponding geometric parameters when the performance is better are determined; The propagation behavior of microwave in the circulator is intuitively displayed by electric field distribution diagram and energy flow direction diagram. It is very helpful for students to establish the physical image of directional transmission of microwave by circulator. Related Articles | Metrics | Comments（0）

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Ideological and political exploration of college physics  curriculum based on the cultivation of scientific cognitive ability — taking polarization of light as an example ZHANG Ling-li, WANG Xiao-ou, HUANG Xi-qiang, LIU Zhi-guo, CAO Yong-yin, WANG Xian-jie College Physics    2023, 42 (3): 33-.   DOI: 10.16854/j.cnki.1000-0712.220179 Abstract （891）      PDF（pc） （978KB）（476）       Knowledge map    Save  Taking polarization of light as an example, the discussion on teaching of college physics course and ideological and political mode based on physical process is introduced, and the ideological and political strategy of college physics curriculum with the cultivation of scientific cognitive ability as the core are explored. Taking polarization phenomenon as the lead, its physical principle is explored, and then the related theoretical knowledge of light polarization is given. Finally, it expands the applications of polarizing devices and astronomical compasses of polarized light, as well as the application of scientific and technological frontiers such as the observation of polarized light by FAST. The whole teaching process accords with the order of scientific cognition, cultivating students- ability of scientific thinking and scientific research in imperceptible way, reflects the core of ideological and political education in physics courses of science and technology universities. Related Articles | Metrics | Comments（0）

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Visualization of three－dimensional hydrogen atom electron cloud based on Monte Carlo simulation CAO Yu-han, LU Heng-xin, XIONG Tian-yu, LU Zi-xuan, E Yi-ting, XU Lei, SHU Song College Physics    2022, 41 (6): 78-.   DOI: 10.16854 /j.cnki.1000-0712.210548 Abstract （863）      PDF（pc） （560KB）（433）       Knowledge map    Save This paper introduces a method to visualize the three－dimensional “electron cloud”of hydrogen atom by Monte Carlosimulation． According to the wave function of the electron in hydrogen atom，the visualization of three－dimensional electron cloud of hydrogen atom with different energy levels is realized by using Mathematica software and Monte Carlo simulation method，which makes people have a more intuitive understanding of the behav-ior of the electron in hydrogenatom． At the same time，this paper also gives a universal algorithm based on Monte Carlo method to study the electron cloud image of the general atomic system，including the perturbation system， which can be used for the further development of the visualization resources for the courses of quantum mechanics． Related Articles | Metrics | Comments（0）

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The elastic analysis of Wilberforce pendulum: characteristic derivation  and verification of cylindrical spiral spring model LIU Tian-heng, CAO Bo-xing, ZHANG Fu-lin College Physics    2022, 41 (12): 43-.   DOI: 10.16854/j.cnki.1000-0712.210589 Abstract （859）      PDF（pc） （364KB）（443）       Knowledge map    Save The Wilberforce pendulum is a special coupled system,which is a combination of a vertically suspended cylindrical helical spring and an object fixed at the end of it. The block has two degrees of freedom: the displacement stretching along the central axis of the spring the angular displacement twisting around the central axis of the spring. Its translational kinetic energy and rotational kinetic energy can transform periodically during the viberation at a special set of parameters. The Wilberforce pendulum in question 12 of iypt2021 is studied. In this work，the Lagrange function of the system is given, and the motion equation describing the coupling phenomenon is obtained. Using the natural coordinate system of cylindrical helix, the model of cylindrical helix spring is established. From the perspective of theory of elasticity, the spring model is analyzed by microelement. The geometric meaning of the curvature and torsion of the cylindrical helix is connected with the physical meaning of the spring material strain, and the analytical solution of the spring elastic potential energy is obtained. The mathematical calculation of this method is strict and universal, and can be extended to all kinds of precision calculation related to homogeneous spring mechanics. The static experiment is also carried out, and the theoretical value of the elastic coefficient falls within the range of the synthetic standard uncertainty of the experimental value, which verifies the correctness of the cylindrical coil spring model. Related Articles | Metrics | Comments（0）

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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 （843）      PDF（pc） （763KB）（332）       Knowledge map    Save 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.  Related Articles | Metrics | Comments（0）

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Dispersion relation of one dimensional j-atom chain lattice vibration ZHENG Shi-yan, YUAN Yi-pu, CHANG Dou-liang College Physics    2022, 41 (5): 13-.   DOI: 10.16854/j.cnki.1000-0712.210340 Abstract （838）      PDF（pc） （454KB）（849）       Knowledge map    Save In this paper, lattice vibration of one-dimensional j-atom chain is taken as the theoretical calculation model, and its equations are obtained under the harmonic and the nearest adjacent approximation. By setting j=1, 2, and 3, respectively, the dispersion relations of one-dimensional single atom, two atoms and three atoms chain lattice vibration are derived which are the same as those in the existing textbooks and references. The results have shown that the equations of one-dimensional j-atom chain lattice vibration obtained in this paper are general. Then starting from this set of equations, the influence of typical crystal structure parameters (such as atomic distance, restoring force coefficient, and atomic mass) on the dispersion relations of one-dimensional four atoms chain lattice vibration is analyzed by numerical simulation, which intensifies the impact of related content of lattice vibration in solid-state physics, and provides a certain reference value for the fabrication of band-pass filters in engineering. Related Articles | Metrics | Comments（0）

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features of electrodes current of Franck-Hertz tube JIANG Xiong-fei, LU Chang-hong, LI Zhen, LI Cheng-kai, LI Yu-han College Physics    2022, 41 (12): 60-.   DOI: 10.16854/j.cnki.1000-0712.220170 Abstract （784）      PDF（pc） （509KB）（151）       Knowledge map    Save  The measurement of the electrode current of argon-filled Frank-Hertz (F-H) tube shows that most of the electrons emitted by cathode are absorbed by grid1 and grid2, and only a small fraction forms the plate current. The grid1 and grid2 voltages have a significant influence on the number of electrons emitted by the cathode. Grid1 can not only absorb electrons, but also emit electrons under certain conditions. The direct reason why the F-H curve first increases and then decreases with grid1 voltage is given. The explanation of electron energy distribution with non-zero valley current of F-H curve is also given. Related Articles | Metrics | Comments（0）